Measurement of neutral current cross sections at …arXiv:hep-ex/0608014v2 10 Aug 2006 DESY 06-116 July, 2006 Measurement of neutral current cross sections at high Bjorken-x with the

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ep-e

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4v2

10

Aug

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DESY 06-116

July, 2006

Measurement of neutral current cross

sections at high Bjorken-x with the ZEUS

detector at HERA

ZEUS Collaboration

Abstract

A new method is employed to measure the neutral current cross section up to

Bjorken-x values of one with the ZEUS detector at HERA using an integrated

luminosity of 65.1 pb−1 for e+p collisions and 16.7 pb−1 for e−p collisions at√s = 318 GeV and 38.6 pb−1 for e+p collisions at

√s = 300 GeV. Cross

sections have been extracted for Q2 ≥ 648 GeV2 and are compared to predictions

using different parton density functions. For the highest x bins, the data have

a tendency to lie above the expectations using recent parton density function

parametrizations.

http://arxiv.org/abs/hep-ex/0608014v2

The ZEUS Collaboration

S. Chekanov, M. Derrick, S. Magill, S. Miglioranzi1, B. Musgrave, D. Nicholass1, J. Repond,

R. Yoshida

Argonne National Laboratory, Argonne, Illinois 60439-4815, USA n

M.C.K. Mattingly

Andrews University, Berrien Springs, Michigan 49104-0380, USA

N. Pavel †, A.G. Yagues Molina

Institut fur Physik der Humboldt-Universitat zu Berlin, Berlin, Germany

S. Antonelli, P. Antonioli, G. Bari, M. Basile, L. Bellagamba, M. Bindi, D. Boscherini,

A. Bruni, G. Bruni, L. Cifarelli, F. Cindolo, A. Contin, M. Corradi2, S. De Pasquale,

G. Iacobucci, A. Margotti, R. Nania, A. Polini, L. Rinaldi, G. Sartorelli, A. Zichichi

University and INFN Bologna, Bologna, Italy e

G. Aghuzumtsyan, D. Bartsch, I. Brock, S. Goers, H. Hartmann, E. Hilger, H.-P. Jakob,

M. Jungst, O.M. Kind, E. Paul3, J. Rautenberg4, R. Renner, U. Samson5, V. Schonberg,

M. Wang, M. Wlasenko

Physikalisches Institut der Universitat Bonn, Bonn, Germany b

N.H. Brook, G.P. Heath, J.D. Morris, T. Namsoo

H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom m

M. Capua, S. Fazio, A. Mastroberardino, M. Schioppa, G. Susinno, E. Tassi

Calabria University, Physics Department and INFN, Cosenza, Italy e

J.Y. Kim6, K.J. Ma7

Chonnam National University, Kwangju, South Korea g

Z.A. Ibrahim, B. Kamaluddin, W.A.T. Wan Abdullah

Jabatan Fizik, Universiti Malaya, 50603 Kuala Lumpur, Malaysia r

Y. Ning, Z. Ren, F. Sciulli

Nevis Laboratories, Columbia University, Irvington on Hudson, New York 10027 o

J. Chwastowski, A. Eskreys, J. Figiel, A. Galas, M. Gil, K. Olkiewicz, P. Stopa, L. Zaw-

iejski

The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences,

Cracow, Poland i

L. Adamczyk, T. Bo ld, I. Grabowska-Bo ld, D. Kisielewska, J. Lukasik, M. Przybycien,

L. Suszycki

Faculty of Physics and Applied Computer Science, AGH-University of Science and Tech-

nology, Cracow, Poland p

I

A. Kotanski8, W. S lominski

Department of Physics, Jagellonian University, Cracow, Poland

V. Adler, U. Behrens, I. Bloch, A. Bonato, K. Borras, N. Coppola, J. Fourletova, A. Geiser,

D. Gladkov, P. Gottlicher9, I. Gregor, O. Gutsche, T. Haas, W. Hain, C. Horn, B. Kahle,

U. Kotz, H. Kowalski, H. Lim10, E. Lobodzinska, B. Lohr, R. Mankel, I.-A. Melzer-

Pellmann, A. Montanari, C.N. Nguyen, D. Notz, A.E. Nuncio-Quiroz, R. Santamarta,

U. Schneekloth, A. Spiridonov11, H. Stadie, U. Stosslein, D. Szuba12, J. Szuba13, T. Theedt,

G. Watt, G. Wolf, K. Wrona, C. Youngman, W. Zeuner

Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

S. Schlenstedt

Deutsches Elektronen-Synchrotron DESY, Zeuthen, Germany

G. Barbagli, E. Gallo, P. G. Pelfer

University and INFN, Florence, Italy e

A. Bamberger, D. Dobur, F. Karstens, N.N. Vlasov14

Fakultat fur Physik der Universitat Freiburg i.Br., Freiburg i.Br., Germany b

P.J. Bussey, A.T. Doyle, W. Dunne, J. Ferrando, D.H. Saxon, I.O. Skillicorn

Department of Physics and Astronomy, University of Glasgow, Glasgow, United King-

dom m

I. Gialas15

Department of Engineering in Management and Finance, Univ. of Aegean, Greece

T. Gosau, U. Holm, R. Klanner, E. Lohrmann, H. Salehi, P. Schleper, T. Schorner-Sadenius,

J. Sztuk, K. Wichmann, K. Wick

Hamburg University, Institute of Exp. Physics, Hamburg, Germany b

C. Foudas, C. Fry, K.R. Long, A.D. Tapper

Imperial College London, High Energy Nuclear Physics Group, London, United King-

dom m

M. Kataoka16, T. Matsumoto, K. Nagano, K. Tokushuku17, S. Yamada, Y. Yamazaki

Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japan f

A.N. Barakbaev, E.G. Boos, A. Dossanov, N.S. Pokrovskiy, B.O. Zhautykov

Institute of Physics and Technology of Ministry of Education and Science of Kazakhstan,

Almaty, Kazakhstan

D. Son

Kyungpook National University, Center for High Energy Physics, Daegu, South Korea g

II

J. de Favereau, K. Piotrzkowski

Institut de Physique Nucleaire, Universite Catholique de Louvain, Louvain-la-Neuve, Bel-

gium q

F. Barreiro, C. Glasman18, M. Jimenez, L. Labarga, J. del Peso, E. Ron, J. Terron,

M. Zambrana

Departamento de Fısica Teorica, Universidad Autonoma de Madrid, Madrid, Spain l

F. Corriveau, C. Liu, R. Walsh, C. Zhou

Department of Physics, McGill University, Montreal, Quebec, Canada H3A 2T8 a

T. Tsurugai

Meiji Gakuin University, Faculty of General Education, Yokohama, Japan f

A. Antonov, B.A. Dolgoshein, I. Rubinsky, V. Sosnovtsev, A. Stifutkin, S. Suchkov

Moscow Engineering Physics Institute, Moscow, Russia j

R.K. Dementiev, P.F. Ermolov, L.K. Gladilin, I.I. Katkov, L.A. Khein, I.A. Korzhavina,

V.A. Kuzmin, B.B. Levchenko19, O.Yu. Lukina, A.S. Proskuryakov, L.M. Shcheglova,

D.S. Zotkin, S.A. Zotkin

Moscow State University, Institute of Nuclear Physics, Moscow, Russia k

I. Abt, C. Buttner, A. Caldwell, D. Kollar, W.B. Schmidke, J. Sutiak

Max-Planck-Institut fur Physik, Munchen, Germany

G. Grigorescu, A. Keramidas, E. Koffeman, P. Kooijman, A. Pellegrino, H. Tiecke,

M. Vazquez20, L. Wiggers

NIKHEF and University of Amsterdam, Amsterdam, Netherlands h

N. Brummer, B. Bylsma, L.S. Durkin, A. Lee, T.Y. Ling

Physics Department, Ohio State University, Columbus, Ohio 43210 n

P.D. Allfrey, M.A. Bell, A.M. Cooper-Sarkar, A. Cottrell, R.C.E. Devenish, B. Foster,

C. Gwenlan21, K. Korcsak-Gorzo, S. Patel, V. Roberfroid22, A. Robertson, P.B. Straub,

C. Uribe-Estrada, R. Walczak

Department of Physics, University of Oxford, Oxford United Kingdom m

P. Bellan, A. Bertolin, R. Brugnera, R. Carlin, R. Ciesielski, F. Dal Corso, S. Dusini,

A. Garfagnini, S. Limentani, A. Longhin, L. Stanco, M. Turcato

Dipartimento di Fisica dell’ Universita and INFN, Padova, Italy e

B.Y. Oh, A. Raval, J.J. Whitmore

Department of Physics, Pennsylvania State University, University Park, Pennsylvania

16802 o

Y. Iga

Polytechnic University, Sagamihara, Japan f

III

G. D’Agostini, G. Marini, A. Nigro

Dipartimento di Fisica, Universita ’La Sapienza’ and INFN, Rome, Italy e

J.E. Cole, J.C. Hart

Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, United Kingdom m

H. Abramowicz23, A. Gabareen, R. Ingbir, S. Kananov, A. Levy

Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel-Aviv

University, Tel-Aviv, Israel d

M. Kuze

Department of Physics, Tokyo Institute of Technology, Tokyo, Japan f

R. Hori, S. Kagawa24, S. Shimizu, T. Tawara

Department of Physics, University of Tokyo, Tokyo, Japan f

R. Hamatsu, H. Kaji, S. Kitamura25, O. Ota, Y.D. Ri

Tokyo Metropolitan University, Department of Physics, Tokyo, Japan f

M.I. Ferrero, V. Monaco, R. Sacchi, A. Solano

Universita di Torino and INFN, Torino, Italy e

M. Arneodo, M. Ruspa

Universita del Piemonte Orientale, Novara, and INFN, Torino, Italy e

S. Fourletov, J.F. Martin

Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7 a

S.K. Boutle15, J.M. Butterworth, R. Hall-Wilton20, T.W. Jones, J.H. Loizides, M.R. Sutton26,

C. Targett-Adams, M. Wing

Physics and Astronomy Department, University College London, London, United King-

dom m

B. Brzozowska, J. Ciborowski27, G. Grzelak, P. Kulinski, P. Luzniak28, J. Malka28, R.J. Nowak,

J.M. Pawlak, T. Tymieniecka, A. Ukleja29, J. Ukleja30, A.F. Zarnecki

Warsaw University, Institute of Experimental Physics, Warsaw, Poland

M. Adamus, P. Plucinski31

Institute for Nuclear Studies, Warsaw, Poland

Y. Eisenberg, I. Giller, D. Hochman, U. Karshon, M. Rosin

Department of Particle Physics, Weizmann Institute, Rehovot, Israel c

E. Brownson, T. Danielson, A. Everett, D. Kcira, D.D. Reeder, P. Ryan, A.A. Savin,

W.H. Smith, H. Wolfe

Department of Physics, University of Wisconsin, Madison, Wisconsin 53706, USA n

IV

S. Bhadra, C.D. Catterall, Y. Cui, G. Hartner, S. Menary, U. Noor, M. Soares, J. Standage,

J. Whyte

Department of Physics, York University, Ontario, Canada M3J 1P3 a

V

1 also affiliated with University College London, UK2 also at University of Hamburg, Germany, Alexander von Humboldt Fellow3 retired4 now at Univ. of Wuppertal, Germany5 formerly U. Meyer6 supported by Chonnam National University in 20057 supported by a scholarship of the World Laboratory Bjorn Wiik Research Project8 supported by the research grant no. 1 P03B 04529 (2005-2008)9 now at DESY group FEB, Hamburg, Germany10 now at Argonne National Laboratory, Argonne, IL, USA11 also at Institut of Theoretical and Experimental Physics, Moscow, Russia12 also at INP, Cracow, Poland13 on leave of absence from FPACS, AGH-UST, Cracow, Poland14 partly supported by Moscow State University, Russia15 also affiliated with DESY16 now at ICEPP, University of Tokyo, Japan17 also at University of Tokyo, Japan18 Ramon y Cajal Fellow19 partly supported by Russian Foundation for Basic Research grant no. 05-02-39028-

NSFC-a20 now at CERN, Geneva, Switzerland21 PPARC Postdoctoral Research Fellow22 EU Marie Curie Fellow23 also at Max Planck Institute, Munich, Germany, Alexander von Humboldt Research

Award24 now at KEK, Tsukuba, Japan25 Department of Radiological Science26 PPARC Advanced fellow27 also at Lodz University, Poland28 Lodz University, Poland29 supported by the Polish Ministry for Education and Science grant no. 1 P03B 1262930 supported by the KBN grant no. 2 P03B 1272531 supported by the Polish Ministry for Education and Science grant no. 1 P03B 14129

† deceased

VI

a supported by the Natural Sciences and Engineering Research Council of

Canada (NSERC)b supported by the German Federal Ministry for Education and Research

(BMBF), under contract numbers HZ1GUA 2, HZ1GUB 0, HZ1PDA 5,

HZ1VFA 5c supported in part by the MINERVA Gesellschaft fur Forschung GmbH, the Is-

rael Science Foundation (grant no. 293/02-11.2) and the U.S.-Israel Binational

Science Foundationd supported by the German-Israeli Foundation and the Israel Science Foundatione supported by the Italian National Institute for Nuclear Physics (INFN)f supported by the Japanese Ministry of Education, Culture, Sports, Science

and Technology (MEXT) and its grants for Scientific Researchg supported by the Korean Ministry of Education and Korea Science and Engi-

neering Foundationh supported by the Netherlands Foundation for Research on Matter (FOM)i supported by the Polish State Committee for Scientific Research,

grant no. 620/E-77/SPB/DESY/P-03/DZ 117/2003-2005 and grant no.

1P03B07427/2004-2006j partially supported by the German Federal Ministry for Education and Re-

search (BMBF)k supported by RF Presidential grant N 1685.2003.2 for the leading scientific

schools and by the Russian Ministry of Education and Science through its

grant for Scientific Research on High Energy Physicsl supported by the Spanish Ministry of Education and Science through funds

provided by CICYTm supported by the Particle Physics and Astronomy Research Council, UKn supported by the US Department of Energyo supported by the US National Science Foundationp supported by the Polish Ministry of Scientific Research and Information Tech-

nology, grant no. 112/E-356/SPUB/DESY/P-03/DZ 116/2003-2005 and 1

P03B 065 27q supported by FNRS and its associated funds (IISN and FRIA) and by an

Inter-University Attraction Poles Programme subsidised by the Belgian Federal

Science Policy Officer supported by the Malaysian Ministry of Science, Technology and Innova-

tion/Akademi Sains Malaysia grant SAGA 66-02-03-0048

VII

1 Introduction

Only limited information is available on structure functions at high Bjorken-x in the deep

inelastic scattering (DIS) regime. This is largely due to limitations in beam energies, in

measurement techniques and the small cross section at high x. In this paper, a new method

is described and used to measure the neutral current (NC) cross section in electron-proton

scattering up to x = 1 with data from the ZEUS detector at HERA.

At HERA, proton beams of 920 GeV (820 GeV prior to 1998), collide with either electron

or positron beams of 27.5 GeV. The electron1 interacts with the proton via the exchange of

a gauge boson. The description of DIS is usually given in terms of three Lorentz-invariant

quantities, Q2, x and y, which are related by Q2 = sxy, where the masses of the electron

and proton are neglected, s is the square of the center-of-mass energy, Q2 is the negative

of the square of the transferred four-momentum, x is the Bjorken variable [1] and y is

the inelasticity. The NC electron-proton differential scattering cross section is typically

written in terms of the proton structure functions as

d2σSMBorn(e±p)

dx dQ2=

2πα2

xQ4

[

Y+F2

(

x,Q2)

∓ Y−xF3

(

x,Q2)

− y2FL

(

x,Q2)]

, (1)

where Y± ≡ 1 ± (1 − y)2 and α denotes the fine-structure constant. At leading order

(LO) in QCD, the longitudinal structure function, FL, is zero and the structure functions

F2 and xF3 can be expressed as products of electroweak couplings and parton density

functions (PDFs).

The form of the PDFs is typically parametrized as q(x) = Ax−λf(x)(1 − x)η, where f(x)

interpolates between the low-x and high-x domains. Such a form allows for an accurate

description of the data at low x [2–6]. For x ≥ 0.3, the PDFs are found to decrease

very quickly. However, a direct confrontation with data has not been possible to date for

x → 1. The highest measured points in the DIS regime are for x = 0.75 [7]. Data at

higher x exist [8,9] but these are in the resonance production region and cannot be easily

interpreted in terms of parton distributions. The highest x value for HERA structure

function data reported to date is x = 0.65 [4, 5]. The differences between different PDF

sets increase rapidly as x increases, even though they use similar data and have common

parametrization for x → 1. The uncertainties for x > 0.75 are large and hard to quantify.

This paper presents a reanalysis of previously published ZEUS data [4,10,11] with a new

reconstruction technique designed to extract cross sections extending up to x = 1 at high

Q2. The data correspond to an integrated luminosity of 38.6 pb−1 for e+p collisions at

1 In the following, we use the term electron to represent both electrons and positrons unless specifically

noted otherwise.

1

√s = 300 GeV recorded in 96-97, 16.7 pb−1 for e−p collisions at

√s = 318 GeV recorded

in 98-99 and 65.1 pb−1 for e+p collisions at√s = 318 GeV recorded in 99-00.

2 The ZEUS experiment at HERA

ZEUS is a multipurpose detector described elsewhere [12]. A schematic depiction of the

ZEUS detector is given in Fig. 1. A brief outline of the components that are most relevant

for this analysis is given below.

The high-resolution uranium–scintillator calorimeter (CAL) [13] consists of three parts:

the forward (FCAL), the barrel (BCAL) and the rear (RCAL) calorimeters. Each part

is divided into modules and further subdivided into towers; each tower is longitudinally

segmented into one electromagnetic section (EMC) and either one (in RCAL) or two (in

BCAL and FCAL) hadronic sections (HAC). The smallest subdivision of the calorimeter

is called a cell. The CAL energy resolutions, measured under test-beam conditions, are

σ(E)/E = 0.18/√E for electrons and σ(E)/E = 0.35/

√E for hadrons, with E in GeV.

The timing resolution of the CAL is ∼ 1 ns for energy deposits larger than 4.5 GeV.

Charged particles are tracked in the central tracking detector (CTD) [14], which operates

in a magnetic field of 1.43 T provided by a thin superconducting solenoid. The CTD

consists of 72 cylindrical drift-chamber layers, organized in nine superlayers covering the

polar-angle2 region 15◦ < θ < 164◦. The transverse-momentum resolution for full-length

tracks is σ(pT )/pT = 0.0058 pT ⊕ 0.0065 ⊕ 0.0014/pT , with pT in GeV.

The luminosity is measured using the Bethe-Heitler reaction ep → eγp [15]. The re-

sulting small-angle photons were measured by the luminosity monitor, a lead-scintillator

calorimeter placed in the HERA tunnel 107 m from the interaction point in the electron

beam direction.

3 New reconstruction method

Figure 1 also shows a schematic depiction of a high-Q2 NC event in the ZEUS detector:

a scattered electron and a jet are outlined in the CAL, while the proton remnant largely

disappears down the forward beam pipe. The electron is typically scattered at a large

angle and is easily recognized in the detector. Such events have been analyzed by a

2 The ZEUS coordinate system is a right-handed Cartesian system, with the Z axis pointing in the

proton beam direction, referred to as the “forward direction”, and the X axis pointing left towards

the center of HERA. The coordinate origin is at the nominal interaction point.

2

variety of techniques in the past, such as the double-angle method, all of which limited

the maximum value of x which could be measured. In the new techniques presented here,

the hadronic system can be used to measure x by reconstructing the energy and angle of

the jet produced by the scattered quark. Above some x value that depends on Q2, the

jet is at a small angle and not well reconstructed. An integrated cross section above an x

cut value is then measured.

The scattered electron was identified and reconstructed by combining calorimeter and

CTD information [16]. The algorithm starts by identifying CAL clusters topologically

consistent with an electromagnetic shower. If the electron candidate was in the range

23◦ < θe < 156◦, a well reconstructed matched track was required. The scattered-electron

energy, E ′e, was determined from the calorimeter energy deposit and was corrected for the

energy lost in inactive material in front of the CAL. The electron energy resolution was

5% for E ′e > 20 GeV. The electron angle θe was determined using the matched track,

when available, and the position of the calorimeter cluster and the event vertex if the

electron was outside the CTD acceptance. The electron angular resolution was 2 mrad

for θe < 23◦, 3 mrad for 23◦ < θe < 156◦ and 5 mrad for θe > 156◦ [4].

Jets were reconstructed from the remaining clusters with the longitudinally invariant kTcluster algorithm [17] in the inclusive mode [18]. Each cluster energy was corrected for

energy loss in dead material, and clusters identified as backsplash [16] from the FCAL

into the BCAL or RCAL were rejected. The jet variables were defined according to the

Snowmass convention [19]:

ET,jet =∑

i

ET,i , ηjet =

∑

i ET,iηiET,jet

,

θjet = 2 tan−1(e−ηjet) , Ejet =∑

i

Ei,

where Ei, ET,i and ηi are the energy, transverse energy and pseudorapidity of the CAL

clusters. The jet energy and angular resolutions were σEjet/Ejet = 55%/

√

Ejet ⊕ 2% and

σθjet/θjet = 1.6% ⊕ 1.9%/√

θjet [20].

Events were first sorted into Q2 bins using information from the electron only:

Q2 = 2EeE′e(1 + cos θe),

where Ee is the electron beam energy. The electron was well reconstructed in the whole

kinematic region, yielding a relative resolution in Q2 for all x of about 5%. The jet

information was then used to calculate x for events with a well reconstructed jet:

x =Ejet(1 + cos θjet)

2Ep(1 − Ejet(1−cos θjet)

2Ee

),

3

where Ep is the proton beam energy. The relative resolution in x varied from 15% to

4% as x increased from 0.06 to 0.7 in events where a jet could be reconstructed. At

high x, θjet is small and x ≈ Ejet/Ep, where Ejet has good resolution. The events with a

reconstructed jet were sorted into x bins to allow a measurement of the double differential

cross-section d2σBorn/dxdQ2. Events with no jet reconstructed within the fiducial volume

were assumed to come from high x and were collected in a bin with xedge < x < 1. An

integrated cross section was calculated from∫ 1

xedge(d2σBorn/dxdQ

2)dx. Due to their poorer

x resolution, events with more than one jet were discarded. The correction to the cross

section for multi-jet events was taken from the Monte Carlo simulation described below,

and ranged from 9% at x = 0.1 to 1% at x = 0.6. The systematic uncertainty associated

with this cut is discussed in Section 6.2.2. More details of this reconstruction technique

are given elsewhere [21].

4 Monte Carlo simulations

Monte Carlo (MC) simulations were used to evaluate the efficiency for selecting events,

for determining the accuracy of the kinematic reconstruction, and for estimating the

background rate. The statistical uncertainties from the MC samples were negligible in

comparison to those of the data.

Standard Model (SM) NC DIS events were simulated with DjangoH version 1.1 [22]

which includes an interface to the Heracles 4.6.1 [23] program. Heracles includes the

corrections for the initial- and final-state electroweak radiation, vertex and propagator

corrections, and two-boson exchange. The hadronic final state was simulated using the

Meps model of Lepto 6.5 [24], which includes order-αS matrix elements (ME) with a

lower and upper cutoff on the soft and collinear divergences. Both the ME cut-offs and the

parton evolutions are treated by parton showers based on the DGLAP evolution equations.

The fragmentation of the scattered partons into observable hadrons is performed with the

Lund string hadronization model by Jetset [25]. The CTEQ6D PDF set [3] was used.

The ZEUS detector response was simulated using a program based on Geant 3.13 [26].

The generated events were passed through the detector simulation, subjected to the same

trigger requirements as the data and processed by the same reconstruction programs.

The vertex distribution in data is a crucial input to the MC simulation for the correct

evaluation of the event-selection efficiency. Therefore, the Z-vertex distribution used in

the MC simulation was determined from a sample of NC DIS events in which the event-

selection efficiency was independent of the Z position of the event vertex [4].

4

5 Event selection

5.1 Trigger

ZEUS operates a three-level trigger system [4,27]. At the first-level, only coarse calorime-

ter and tracking information are available. Events were selected using criteria based on

energy deposits in the CAL consistent with an isolated electron. In addition, events with

high ET in coincidence with a CTD track were accepted. At the second level, a cut on

δ > 29 GeV was imposed to select NC events, with δ defined as:

δ ≡∑

i

(E − pZ)i =∑

i

(Ei −Ei cos θi) ,

where the sum runs over all calorimeter energy deposits Ei with polar angles θi. Timing

information from the calorimeter was used to reject events inconsistent with the bunch-

crossing time. At the third level, events were fully reconstructed and selected according

to requirements similar to, but looser than, the offline cuts described below.

The main uncertainty in the trigger efficiency comes from the first level. The efficiency

in data and MC simulation agreed to within ∼ 0.5% and the overall efficiency was above

95%.

5.2 Offline selection

The following criteria were imposed to select NC DIS events offline:

• an electron with E ′e > 25 GeV was required. An isolation cut was imposed by requiring

that less than 4 GeV be deposited in calorimeter cells not associated with the scattered

electron in an η-φ cone of radius Rcone = 0.8 centered on the candidate cluster. For

those electrons in the CTD acceptance, a matched track was required which passed

within 10 cm of the cluster center. The matched track was required to traverse at

least four of the nine superlayers of the CTD. The momentum of the track, ptrk, had

to be at least 10 GeV. For electrons outside the forward tracking acceptance of the

CTD, the tracking requirement in the electron selection was replaced by a cut on the

transverse momentum of the electron, pT,e > 30 GeV;

• a fiducial-volume cut was applied to the electron to guarantee that the experimental

acceptance was well understood. It excluded the transition regions between the FCAL

and the BCAL [28]. It also excluded the regions within 1.5 cm of the module gaps in

the BCAL. As the kinematic region considered in this analysis is at high Q2, events

with electrons in the RCAL were discarded.

5

The following cuts were used to select an essentially background free and well recon-

structed event sample:

• either 0 or 1 valid jets. Valid jets were required to have ET,jet > 10 GeV and

θjet > 0.12 rad;

• a reconstructed vertex with −50 < Zvtx < 50 cm, a range consistent with ep interac-

tions;

• δ > 40 GeV to suppress photoproduction events, in which the scattered electron

escaped through the beam hole in the RCAL. This cut value was δ > 47 GeV for

events in the highest x bins. This cut also rejected events with large initial-state QED

radiation. In addition, δ < 65 GeV was required to remove “overlay” events in which

a normal DIS event coincided with additional energy deposits in the RCAL from some

other reaction. This requirement had a negligible effect on the efficiency for selecting

NC DIS events.

• ye < 0.95 to further reduce background from photoproduction events, where ye was

defined as

ye = 1 − E ′e

2Ee

(1 − cos θe);

• PT/√ET < 4

√GeV to remove cosmic rays and beam-related backgrounds. The vari-

ables PT and ET were defined by:

P 2T = P 2

X + P 2Y = (

∑

i

Ei sin θi cosφi)2 + (

∑

i

Ei sin θi sin φi)2,

ET =∑

i

Ei sin θi,

where the sums run over all calorimeter energy deposits, Ei, with polar and azimuthal

angles θi and φi with respect to the event vertex, respectively;

• ≥ 5 HAC cells with energy above 110 MeV to remove elastic Compton scattering

events (ep → eγp) and further reduce the size of the QED radiative corrections. The

contribution from deeply virtual Compton scattering was found to be negligible;

• yJB < 1.3 ·Q2edge/(s ·xedge) to limit event migration from small x to large x for zero-jet

events. The variable yJB was calculated with the Jacquet-Blondel method [29]. The

quantities xedge and Q2edge are the lower x and upper Q2 edges of the bins defined for

the cross-section measurement (see Section 6.1).

After these selections, 10298 events remained in the 99-00 e+p data, 2664 in the 98-99

e−p data and 5935 in the 96-97 e+p data in the bins used to extract the cross sections.

The numbers of events in the zero-jet bins were 1292, 293 and 493, respectively.

6

Monte Carlo distributions are compared with those from data in Figs. 2-5 for several

variables. The MC distributions are normalized to the measured luminosity. Only the

comparison to 99-00 e+p data is shown; the comparisons of 98-99 e−p and 96-97 e+p data

with MC distributions show similar features. The first set of plots, Fig. 2, shows general

properties for the full sample of events. Good agreement between data and MC simulation

is observed, with no indication of residual backgrounds. The small disagreement observed

in Fig. 2c has been verified to have negligible impact on the results presented in this

paper. Figure 3 shows distributions related to the scattered electron. Figure 4 presents

a series of control plots for jet quantities. The MC reproduces the data distribution for

the number of reconstructed jets to high accuracy. This is important since the MC is

used to correct for the inefficiency resulting from the requirement of zero or one jet in

the event. The remaining distributions in this figure are for the jet quantities in one jet

events. Figure 5 shows distributions for the class of events with zero jets. Overall, 13%

more data events for 99-00 e+p, 2% more data events for 98-99 e−p and 5% more data

events for 96-97 e+p are observed for zero-jet events than expected in the simulation. An

offset in the δ distribution is seen, with the MC distribution slightly lower than the data.

This offset can however be explained by shifting the electron energy scale by 1%, which

is within its estimated uncertainty.

6 Analysis

6.1 Binning, acceptance and cross-section determination

The bins in the (x,Q2) kinematic space used in this analysis are shown in Fig. 6. The bin

widths in Q2 were chosen to correspond to three times the resolution of the reconstructed

Q2. The minimum value of Q2 corresponds roughly to the acceptance of the BCAL.

The lower x edge of the bin for zero-jet events, xedge, was determined from the condition

θjet > 0.12 rad. For the bins where a jet was reconstructed, the bin widths in x were

chosen to correspond to three times the resolution of the reconstructed x.

The MC simulation was used to study the x distribution of the zero-jet events. Figure 7

shows the true x distribution for the 99-00 e+p MC events in different Q2 bins. Similar

distributions are observed in the 98-99 e−p and 96-97 e+p MC. As can be seen in this

figure, the zero-jet events originate predominantly from the interval xedge < x < 1. We

note that these distributions depend on the particular PDF chosen and that there are

uncertainties at large x.

The efficiency, defined as the number of events generated and reconstructed in a bin

after all selection cuts divided by the number of events that were generated in that bin,

7

was typically 40%. In some low-Q2 bins, dominated by events in which the electron is

scattered into the RCAL or the B/RCAL transition region and removed by the fiducial

cut, the efficiency was lower. The purity, defined as the number of events generated

and reconstructed in a bin after all selection cuts divided by the total number of events

reconstructed in that bin, was typically 50%. The efficiency and purity in the (x,Q2) bins

for the 99-00 e+p simulation are shown in Fig. 8. The 96-97 e+p and 98-99 e−p simulations

yielded similar values. The efficiency and purity in zero-jet bins are comparable to those

in the mid-x bins.

The double-differential cross section was determined as

d2σBorn(x,Q2)

dxdQ2=

Ndata(∆x,∆Q2)

NMC(∆x,∆Q2)(1 + δ(Q2))

d2σSMBorn

dxdQ2,

and the integrated cross section was determined as

1∫

xedge

d2σBorn(x,Q2)

dxdQ2dx =

Ndata(∆x,∆Q2)

NMC(∆x,∆Q2)(1 + δ(Q2))

1∫

xedge

d2σSMBorn

dxdQ2dx,

where Ndata(∆x,∆Q2) is the number of data events in a bin (∆x,∆Q2) and NMC(∆x,∆Q2)

is the number of signal MC events normalized to the luminosity of the data. The SM

prediction, d2σSMBorn(x,Q2)/dxdQ2, was evaluated according to Eq. (1) with the same PDF

and electroweak (EW) parameters as used in the MC simulation. This procedure implic-

itly takes the acceptance, bin-centering and leading-order radiative corrections from the

MC simulation. The variation of the cross sections resulting from different choices of PDF

in the MC are described in the next section. The values of (x,Q2) at which the cross

sections are quoted are given in Tables 1-6.

Monte Carlo studies indicated that the radiative corrections have little dependence on

x for the kinematic reconstruction method used here. The correction for higher-order

radiative effects, δ(Q2), calculated from HECTOR [30] varied from 3% at low Q2 to 0%

at high Q2.

6.2 Systematic uncertainties

Systematic uncertainties associated with the MC simulations were estimated by re-calculating

the cross section after modifying the simulation to account for known uncertainties. Cut

values were varied where this method was not applicable.

8

6.2.1 Uncorrelated systematic uncertainties

The following systematic uncertainties are either small or exhibit no bin-to-bin correla-

tions:

• electron energy resolution in the MC simulation. The effect on the cross sections was

evaluated by changing the resolution by ±1% in the MC. This resulted in ±1% effects

over almost the full kinematic range. The effect increased to ±2% for the double-

differential cross section in several low Q2 bins and for several integrated cross section

bins;

• electron angle. Uncertainties in the electron scattering-angle determination are known

to be at most 1 mrad [11]. The resulting systematic effects on the cross-section mea-

surement were at most 2%;

• electron-isolation requirement. Variation of the electron-isolation energy by ±2 GeV

caused negligible effects in the measured cross section in the low-Q2 region and 2.5%

in the high-Q2 region;

• FCAL alignment. The FCAL jet position was varied by ±0.5 cm in both X and Y

directions. The resulting changes in the cross sections were negligible;

• reconstructed-vertex uncertainty. The cut on the reconstructed Z vertex was changed

by ±2 cm; The uncertainties in the cross sections associated with this variation were

negligible over the full kinematic range;

• background uncertainty. The estimated background from all sources was less than 1%

and gave negligible uncertainty.

6.2.2 Correlated systematic uncertainties

The significant correlated systematic uncertainties are listed below and labeled for further

reference. They were determined to result from the following sources:

• {δ1} electron-energy scale. The systematic uncertainty resulting from uncertainty in

the electron energy scale was checked by changing the energy scale by ±1%. This

resulted in typically 2% systematic variations in the cross sections;

• {δ2} jet-energy scale. The uncertainty in the cross sections arising from the measure-

ment of the jet energy was checked by changing the energy scale by ±1%. The effect

in the highest-x bins was negligible over the full Q2 region. The uncertainty in the

double-differential cross-section bins was 0 − 7% for 0.1 < x < 0.7;

9

• {δ3} FCAL first inner ring (FIR) EMC energy scale. The effect of the FIR EMC

energy scale uncertainty on the cross section was checked by changing the energy scale

by ±5%, which gave 0 − 3.5% uncertainty as x increased from 0.1 to 0.9;

• {δ4} different PDFs. The uncertainty in the extracted cross section resulting from

uncertainties in the shape of the PDFs at high x was checked by comparing the cross

sections calculated from different sets: CTEQ4D, CTEQ6D, MRST99, ZEUS-S and

ZEUS-JETS. The effect was less than 1% at low x and increased to 5% at high x;

• {δ5} simulation of the hadronic final state and jet-selection procedure. The invariant

kT jet algorithm was replaced with a cone algorithm [19] with cone radius 0.7, and cross

sections were re-evaluated. The uncertainty was found to be ±1.6% in the highest x

bins and ±2.5% in the lower x bins. In addition, the analysis was redone under the

following conditions: including multijet events for the events with x < xedge; varying

the jet ET and θjet cuts for the jet selection; and varying the yJB cut. These checks

produced small differences consistent with expected statistical variations and were not

included in the systematic uncertainty;

• {δ6} higher order radiative corrections and a possible dependence on x. The uncer-

tainty was estimated to be about 2% at low x, increasing to 12% at x > 0.8;

• {δ7} uncertainties on the luminosity. The uncertainties for the 96-97 e+p sample, 98-99

e−p sample and 99-00 e+p sample are 1.6%, 1.8% and 2.25%, respectively.

6.3 Results

The measured Born level cross sections for 96-97 e+p, 98-99 e−p and 99-00 e+p and their

systematic uncertainties are shown in Tables 1-6. The statistical uncertainties on the cross

sections correspond to the central 68% probability interval evaluated using a Bayesian

approach with flat prior and a Poisson likelihood. For bins with zero measured events,

a 68% probability limit, calculated including the uncorrelated systematic uncertainty, is

given. The cross sections are shown in Figs. 9, 10 and 11 and compared to SM expectations

using the CTEQ6M PDFs [3]. The double differential cross sections are represented by

solid points, and generally agree well with the expectations. The cross section in the

highest-x bins is plotted as

1

1 − xedge

1∫

xedge

d2σBorn

dxdQ2dx .

In these bins, the expected cross section is drawn as a horizontal line, while the mea-

sured cross section is displayed as the open symbol at the center of the bin. The error

10

bars represent the quadratic sum of the correlated systematic uncertainty and the com-

bined statistical and uncorrelated systematic uncertainty determined from the Bayesian

probability analysis.

The ratios of the measured cross sections to the SM expectation using the CTEQ6M PDFs

for 96-97 e+p , 98-99 e−p and 99-00 e+p are shown in Figs. 12, 13 and 14 respectively.

The ratios of the expectations using the ZEUS-S PDF [31] to that using CTEQ6M and

ZEUS-JETS PDF [32] to that using CTEQ6M are also shown. The uncertainty for the

CTEQ6M fit is displayed in the figure as a shaded band. The measured double-differential

cross sections generally agree well with all three sets of expectations. For the highest x

bins, which extend to previously unmeasured kinematic ranges, the data have a tendency

to lie above the expectations.

The data presented here, specifically the zero-jet data at high x, extend the kinematic

coverage for DIS. These results are expected to have a significant impact on the valence-

quark distributions at high x, where little data are available to date. It should however

be noted that there is overlap with the data presented in previous ZEUS publications,

and these new results should therefore not be used simultaneously with the previously

published ZEUS data [4, 10, 11] in fits to extract model parameters. In the kinematic

region of overlap of this technique with the previous ZEUS technique, the extracted cross

sections are in excellent agreement.

7 Summary

This paper has presented a reanalysis of previously published ZEUS data with a new

technique designed for the reconstruction of large x events, which allows for the extraction

of the cross section up to x = 1. In the previously measured kinematic region, the data

and simulation based on the CTEQ6M PDF are in good agreement. The Standard Model

predictions tend to underestimate the data at the highest values of x.

8 Acknowledgments

We are grateful to the DESY directorate for their strong support and encouragement.

We thank the HERA machine group whose outstanding efforts allowed the measurements

presented here. We also wish to express our thanks for the support of the DESY computing

and network services. The design, construction and installation of the ZEUS detector has

been made possible by the efforts of many people not listed as authors.

11

References

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DESY (1993), available on http://www-zeus.desy.de/bluebook/bluebook.html.

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J. Andruszkow et al., Acta Phys. Pol. B 32, 2025 (2001).

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[17] S. Catani et al., Nucl. Phys. B 406, 187 (1993).

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[19] J.E. Huth et al., Research Directions for the Decade. Proceedings of Summer Study

on High Energy Physics, 1990, E.L. Berger (ed.), p. 134. World Scientific (1992).

Also in preprint FERMILAB-CONF-90-249-E.

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[21] Y. Ning, Ph.D. Thesis, Columbia University, (2006), (unpublished).

12

[22] G.A. Schuler and H. Spiesberger, Proc. Workshop on Physics at HERA,

W. Buchmuller and G. Ingelman (eds.), Vol. 3, p. 1419. Hamburg, Germany, DESY

(1991);

H. Spiesberger, heracles and djangoh: Event Generation for ep Interactions at

HERA Including Radiative Processes, 1998, available on

http://www.desy.de/~hspiesb/djangoh.html.

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69, 155 (1992).

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U. Amaldi (ed.), p. 391. Hamburg, Germany (1979). Also in preprint DESY 79/48.

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13

Q2 x d2σ/dxdQ2 N δs δt δu δ1 δ2 δ3 δ4 δ5 δ6

(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

648 0.09 2.66 114 +10−8.5

+7.9−7.8

+2.0−1.6

+6.0−6.1

−0.3+1.2

−0.2+0.1

+1.4−1.4

+2.4−2.4

+3.3−3.3

0.15 1.08 40 +19−13

+8.3−8.7

+2.1−2.2

+6.4−6.7

−1.3+0.4

+1.6−2.1

+0.9−0.9

+2.4−2.4

+3.3−3.3

0.21 7.97 · 10−1 33 +21−15

+11−8.9

+3.6−2.0

+9.2−8.1

−0.4+2.5

+2.7−0.2

+0.5−0.5

+2.4−2.4

+1.0−1.0

761 0.06 3.06 299 +6.1−5.4

+5.0−4.8

+1.3−0.7

+1.0−0.6

−0.4−0.1

−0.4+0.2

+1.7−1.7

+2.4−2.4

+3.3−3.3

0.11 1.72 187 +7.9−6.8

+5.3−5.6

+0.2−1.0

+2.4−3.0

−0.9+1.5

−0.0−0.3

+1.3−1.3

+2.4−2.4

+3.3−3.3

0.16 8.11 · 10−1 92 +12−9.4

+6.2−8.2

+0.8−2.1

+4.2−6.1

−1.4−0.3

+0.3−2.0

+0.8−0.8

+2.4−2.4

+3.3−3.3

0.23 6.09 · 10−1 88 +12−9.6

+6.7−4.5

+0.9−1.5

+4.8−2.8

−0.6+2.6

+1.9+0.5

+0.6−0.6

+2.4−2.4

+1.0−1.0

891 0.07 1.89 314 +6.0−5.4

+4.8−4.7

+1.0−0.3

−0.8+0.8

−0.3+0.3

−0.3+0.3

+1.6−1.6

+2.4−2.4

+3.3−3.3

0.12 9.96 · 10−1 214 +7.3−6.4

+4.8−4.6

+1.2−0.6

+1.1+0.2

−0.9+0.2

+0.0−0.3

+1.2−1.2

+2.4−2.4

+3.3−3.3

0.18 5.96 · 10−1 145 +9.1−7.6

+4.8−4.7

+1.4−0.8

+0.4+0.4

−1.1+0.9

+0.9−1.1

+0.7−0.7

+2.4−2.4

+3.3−3.3

0.25 2.92 · 10−1 91 +12−9.4

+4.0−5.3

+0.7−1.1

+0.5−3.0

−1.9+1.5

+1.6−2.0

+0.8−0.8

+2.4−2.4

+1.0−1.0

1045 0.08 1.16 251 +6.8−5.9

+4.8−4.8

+0.6−0.4

−1.2+1.0

−0.5+0.2

−0.2+0.5

+1.6−1.6

+2.4−2.4

+3.3−3.3

0.13 6.10 · 10−1 182 +8.0−6.9

+4.6−4.8

+0.7−1.1

−0.8+0.2

−1.0+0.8

−0.2−0.3

+1.1−1.1

+2.4−2.4

+3.3−3.3

0.19 3.79 · 10−1 143 +9.1−7.7

+5.4−4.9

+1.3−0.8

−1.7+2.1

+0.2+0.7

+1.9−1.2

+0.6−0.6

+2.4−2.4

+3.3−3.3

0.27 1.94 · 10−1 94 +11−9.3

+4.4−4.4

+2.0−0.5

−0.3+1.1

−2.9+1.8

+1.0−1.0

+0.9−0.9

+2.4−2.4

+1.0−1.0

Table 1: The cross-section table for 96-97 e+p NC scattering. The first twocolumns of the table contain the Q2 and x values at which the cross section isquoted, the third contains the measured cross section d2σ/dxdQ2 corrected to theelectroweak Born level or the upper limit in case of zero observed events, the fourthcontains the number of events reconstructed in the bin, N , the fifth contains thestatistical uncertainty, δs, and the sixth contains the total systematic uncertainty,δt. The right part of the table lists the total uncorrelated systematic uncertainty, δu,followed by the bin-to-bin correlated systematic uncertainties δ1– δ6 defined in thetext. The upper (lower) numbers refer to the variation of the cross section, whereasthe signs of the numbers reflect the direction of change in the cross sections. Notethat the normalization uncertainty, δ7 is not listed.

14

Table 1 (continued):


(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

1224 0.09 7.98 · 10−1 233 +7.0−6.2

+4.8−5.0

+0.0−0.7

−1.6+1.3

−0.2−0.0

−0.5+0.3

+1.6−1.6

+2.4−2.4

+3.3−3.3

0.14 4.26 · 10−1 169 +8.3−7.2

+5.1−4.6

+1.0−0.4

−0.4+2.2

−1.1+0.9

+0.1−0.4

+0.9−0.9

+2.4−2.4

+3.3−3.3

0.21 2.04 · 10−1 91 +12−9.4

+3.9−3.9

+1.8−0.4

+1.0+0.2

−0.4−0.6

+1.1−2.2

+0.6−0.6

+2.4−2.4

+1.0−1.0

0.30 1.25 · 10−1 78 +13−10

+4.7−4.1

+0.6−1.7

−1.7+0.6

−0.7+2.7

+1.8−0.1

+1.1−1.1

+2.4−2.4

+1.0−1.0

1431 0.06 7.68 · 10−1 170 +8.3−7.1

+5.0−5.0

+1.0−0.5

−1.1+1.4

−0.8−0.3

−0.2−0.4

+1.8−1.8

+2.4−2.4

+3.3−3.3

0.10 3.83 · 10−1 126 +9.7−8.1

+5.1−4.8

+1.0−1.2

−0.7+1.6

+1.0+0.4

−0.1+0.5

+1.5−1.5

+2.4−2.4

+3.3−3.3

0.16 2.27 · 10−1 112 +10−8.6

+4.6−5.0

+0.5−0.3

−1.0+0.5

−1.8+0.8

−0.2−0.6

+0.8−0.8

+2.4−2.4

+3.3−3.3

0.23 1.19 · 10−1 70 +13−11

+4.3−3.7

+1.9−0.9

−1.0+2.0

−0.0−0.2

+1.1−1.3

+0.7−0.7

+2.4−2.4

+1.0−1.0

0.32 7.17 · 10−2 59 +15−11

+4.6−4.1

+0.8−0.4

−0.3+0.6

−2.0+2.3

+1.8−1.1

+1.4−1.4

+2.4−2.4

+1.0−1.0

1672 0.07 4.21 · 10−1 126 +9.7−8.1

+5.3−5.0

+1.6−0.5

−1.6+1.9

−0.1+0.1

−0.1−0.1

+1.8−1.8

+2.4−2.4

+3.3−3.3

0.11 3.25 · 10−1 144 +9.1−7.7

+5.0−5.0

+0.6−0.7

−2.0+2.0

−0.3+0.3

−0.3+0.1

+1.3−1.3

+2.4−2.4

+3.3−3.3

0.17 1.35 · 10−1 80 +13−10

+4.5−4.9

+0.4−1.4

−1.3−0.2

−0.8+0.5

+0.2−0.1

+0.7−0.7

+2.4−2.4

+3.3−3.3

0.25 7.96 · 10−2 55 +15−12

+3.3−4.8

+0.3−2.4

−2.0−0.1

−1.5+0.6

+0.6−1.2

+0.8−0.8

+2.4−2.4

+1.0−1.0

0.35 4.27 · 10−2 45 +17−13

+6.4−4.8

+4.1−1.0

−1.7+1.5

−2.1+2.7

+1.5−1.5

+1.8−1.8

+2.4−2.4

+1.0−1.0

1951 0.08 3.32 · 10−1 130 +9.6−8.1

+4.9−5.4

+0.5−1.5

−2.2+1.2

−0.5+0.6

−0.1−0.1

+1.8−1.8

+2.4−2.4

+3.3−3.3

0.13 1.66 · 10−1 86 +12−9.7

+4.7−4.8

+0.9−0.9

−1.2+1.1

−0.6−0.6

−0.3+0.1

+1.2−1.2

+2.4−2.4

+3.3−3.3

0.19 8.47 · 10−2 66 +14−11

+5.3−4.9

+0.9−1.4

−1.6+2.6

−0.7+0.9

+0.1−0.2

+0.7−0.7

+2.4−2.4

+3.3−3.3

0.27 4.53 · 10−2 41 +18−13

+4.2−3.4

+1.6−0.4

−0.3+1.9

−0.6+0.8

+0.9−0.6

+1.0−1.0

+2.4−2.4

+1.0−1.0

0.38 2.69 · 10−2 35 +20−14

+4.8−4.8

+0.3−1.4

−1.3−0.3

−1.8+2.4

+1.8−1.4

+2.2−2.2

+2.4−2.4

+1.0−1.0

2273 0.09 1.88 · 10−1 88 +12−9.6

+4.8−5.4

+0.3−1.5

−2.0+1.1

−0.9+0.4

−0.4−0.0

+1.7−1.7

+2.4−2.4

+3.3−3.3

0.14 8.43 · 10−2 60 +15−11

+5.0−5.0

+0.4−0.7

−2.1+2.1

+0.8−0.5

−0.2+0.2

+1.0−1.0

+2.4−2.4

+3.3−3.3

0.21 6.76 · 10−2 59 +15−11

+3.5−3.9

+0.4−1.0

−0.9+0.1

−1.9+1.4

+0.1−0.4

+0.7−0.7

+2.4−2.4

+1.0−1.0

0.30 3.05 · 10−2 37 +19−14

+4.0−3.8

+1.4−0.7

−0.3+0.9

−1.3+1.3

+0.6−1.1

+1.2−1.2

+2.4−2.4

+1.0−1.0

0.41 1.56 · 10−2 25 +24−16

+6.9−5.2

+2.2−0.7

+1.4+1.0

−1.8+2.6

+3.1−0.5

+2.7−2.7

+2.4−2.4

+2.7−2.7

2644 0.06 1.78 · 10−1 71 +13−11

+5.4−5.5

+0.5−1.3

−2.1+2.5

−0.5+0.0

−0.1−0.6

+2.0−2.0

+2.4−2.4

+3.3−3.3

0.11 9.53 · 10−2 53 +16−12

+4.7−4.8

+0.6−0.7

−1.2+0.4

+0.0+0.7

−0.2+0.1

+1.6−1.6

+2.4−2.4

+3.3−3.3

0.16 6.08 · 10−2 53 +16−12

+4.9−4.8

+0.8−0.5

−1.5+1.8

−0.6+0.5

−0.4−0.1

+0.9−0.9

+2.4−2.4

+3.3−3.3

0.23 3.70 · 10−2 41 +18−13

+3.4−3.7

+0.7−0.7

−0.6+0.6

−1.6+0.7

+0.3−0.4

+0.7−0.7

+2.4−2.4

+1.0−1.0

0.33 1.54 · 10−2 24 +25−17

+5.6−4.9

+3.9−1.9

−2.3+1.1

−0.5+1.2

+1.4−1.7

+1.6−1.6

+2.4−2.4

+1.0−1.0

15



(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

0.45 7.21 · 10−3 13 +36−21

+5.9−7.8

+0.8−3.0

−2.5+0.6

−4.4+2.5

−0.3+1.2

+3.3−3.3

+2.4−2.4

+2.7−2.7

3073 0.07 9.55 · 10−2 51 +16−12

+5.5−5.2

+1.7−1.6

−1.1+2.1

−0.1−0.1

+0.1−0.5

+2.0−2.0

+2.4−2.4

+3.3−3.3

0.12 6.15 · 10−2 42 +18−13

+5.1−5.3

+1.9−1.4

−2.0+1.0

−1.0+0.6

−0.6+0.0

+1.4−1.4

+2.4−2.4

+3.3−3.3

0.18 3.67 · 10−2 40 +19−13

+4.9−5.2

+0.6−0.9

−2.4+2.0

−0.4−0.8

−0.2−0.1

+0.8−0.8

+2.4−2.4

+3.3−3.3

0.26 2.30 · 10−2 31 +21−15

+4.0−3.9

+0.6−0.6

−1.2+0.6

−1.8+2.3

+0.3+0.2

+0.9−0.9

+2.4−2.4

+1.0−1.0

0.36 1.25 · 10−2 24 +25−17

+4.5−4.3

+0.7−0.8

−1.1+0.6

−1.4+2.1

+1.0−0.9

+2.1−2.1

+2.4−2.4

+1.0−1.0

0.49 5.38 · 10−3 13 +36−21

+6.5−7.2

+0.7−1.3

+0.6−0.5

−4.0+3.2

−0.2−1.9

+3.8−3.8

+2.4−2.4

+2.7−2.7

3568 0.09 5.61 · 10−2 39 +19−14

+5.8−5.1

+2.3−0.7

−1.7+2.2

+0.4+0.7

+0.3−0.8

+1.9−1.9

+2.4−2.4

+3.3−3.3

0.14 2.97 · 10−2 27 +23−16

+4.9−6.1

+0.6−3.5

−1.2+1.6

−1.8+0.7

−0.6+0.7

+1.1−1.1

+2.4−2.4

+3.3−3.3

0.21 1.67 · 10−2 22 +26−17

+3.8−3.4

+0.7−0.7

−1.1+1.8

−0.1+0.7

−0.1−0.1

+0.7−0.7

+2.4−2.4

+1.0−1.0

0.29 1.04 · 10−2 19 +29−18

+4.2−3.4

+1.1−0.4

+0.6+1.9

−0.9+1.3

+0.1−0.3

+1.2−1.2

+2.4−2.4

+1.0−1.0

0.40 6.43 · 10−3 16 +32−19

+6.6−5.7

+1.3−0.1

−1.2+4.1

−2.7+1.6

+0.8−1.0

+2.6−2.6

+2.4−2.4

+2.7−2.7

0.53 1.37 · 10−3 4 +79−29

+7.8−7.5

+1.5−0.6

−0.2+1.6

−4.6+4.5

+0.8−0.3

+4.3−4.3

+2.4−2.4

+2.7−2.7

4145 0.10 3.18 · 10−2 26 +24−16

+5.2−6.5

+0.4−3.5

−2.6+2.2

−1.0+0.2

+0.2−0.5

+1.7−1.7

+2.4−2.4

+3.3−3.3

0.16 2.61 · 10−2 32 +21−15

+5.6−5.2

+3.1−1.0

−2.5+1.5

−0.3+0.5

−0.4+0.3

+0.9−0.9

+2.4−2.4

+3.3−3.3

0.23 7.72 · 10−3 14 +35−20

+7.6−4.4

+6.8−1.1

−2.5+0.7

−1.3+1.3

−0.2−0.4

+0.7−0.7

+2.4−2.4

+1.0−1.0

0.33 8.50 · 10−3 20 +28−19

+4.3−4.6

+0.7−1.1

−2.3+1.8

−1.7+1.5

+0.4+0.3

+1.6−1.6

+2.4−2.4

+1.0−1.0

0.44 3.03 · 10−3 9 +46−23

+5.3−13

+0.0−11

−1.6−0.7

−4.0+1.0

+0.5−2.1

+3.3−3.3

+2.4−2.4

+2.7−2.7

0.58 2.96 · 10−4 1 +220−30

+11−7.4

+1.3−2.4

+0.0−2.0

−2.6+7.7

−0.9+4.4

+4.7−4.7

+2.4−2.4

+2.7−2.7

4806 0.12 1.76 · 10−2 18 +30−19

+4.8−7.0

+0.6−5.0

−1.6+1.3

+0.4−0.4

+0.3−0.3

+1.5−1.5

+2.4−2.4

+3.3−3.3

0.18 1.36 · 10−2 20 +28−18

+5.2−4.8

+1.1−0.6

−0.4+1.2

−1.6+2.2

−0.9+0.3

+0.7−0.7

+2.4−2.4

+3.3−3.3

0.26 5.44 · 10−3 12 +38−21

+3.7−3.6

+0.6−0.8

−0.8+1.6

−1.4+0.8

+0.1+0.0

+0.9−0.9

+2.4−2.4

+1.0−1.0

0.36 3.48 · 10−3 10 +43−23

+5.1−4.5

+1.6−0.5

−1.2+2.8

−2.1+1.3

−0.2−0.7

+2.1−2.1

+2.4−2.4

+1.0−1.0

0.49 1.12 · 10−3 4 +79−29

+7.6−6.5

+1.8−0.6

−1.6+2.8

−2.8+3.9

+1.0−0.5

+3.9−3.9

+2.4−2.4

+2.7−2.7

0.63 9.18 · 10−4 4 +79−29

+12−8.1

+1.0−2.0

−2.3−0.3

−4.8+9.6

−1.0+4.8

+4.9−4.9

+2.4−2.4

+0.1−0.1

5561 0.09 2.26 · 10−2 15 +33−20

+6.9−9.6

+1.8−6.5

−4.1+3.5

+3.1−3.1

−0.1−0.5

+1.9−1.9

+2.4−2.4

+3.3−3.3

0.14 1.42 · 10−2 21 +27−17

+5.2−5.2

+0.7−1.4

−2.2+2.5

−0.3+0.6

−0.1−0.4

+1.1−1.1

+2.4−2.4

+3.3−3.3

0.21 3.41 · 10−3 6 +60−26

+3.5−4.2

+0.6−0.9

−2.0+1.5

−1.4−0.3

−0.7+0.3

+0.7−0.7

+2.4−2.4

+1.0−1.0

0.30 4.92 · 10−3 14 +35−20

+4.3−4.4

+0.4−0.7

−2.4+1.1

−1.7+2.5

+0.1−0.3

+1.2−1.2

+2.4−2.4

+1.0−1.0

16



(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

0.41 2.56 · 10−3 9 +46−23

+5.0−5.8

+0.7−1.5

−1.8+0.0

−2.1+1.0

+0.4−0.2

+2.8−2.8

+2.4−2.4

+2.7−2.7

0.54 9.13 · 10−4 4 +79−29

+8.0−8.0

+0.4−2.2

−1.8−0.1

−4.2+5.1

−0.3−1.1

+4.6−4.6

+2.4−2.4

+2.7−2.7

0.69 6.11 · 10−4 3 +96−30

+13−9.9

+5.8−2.1

+0.3+1.8

−7.3+9.2

−3.1+3.1

+4.6−4.6

+2.4−2.4

+0.1−0.1

6966 0.11 6.88 · 10−3 13 +36−21

+6.3−9.9

+0.4−6.6

−4.2+2.3

+3.5−3.6

−0.1−1.5

+1.8−1.8

+2.4−2.4

+3.3−3.3

0.17 6.24 · 10−3 25 +24−16

+4.7−7.8

+0.0−5.3

−2.9+1.7

−2.0+0.3

−0.6−0.2

+0.8−0.8

+2.4−2.4

+3.3−3.3

0.25 2.85 · 10−3 15 +33−20

+3.7−3.7

+0.6−0.8

−1.6+1.8

−0.4+0.8

−0.5+0.0

+0.7−0.7

+2.4−2.4

+1.0−1.0

0.34 2.52 · 10−3 22 +26−17

+4.3−4.3

+0.7−0.8

−1.3+1.9

−1.9+1.3

+0.1−0.1

+1.8−1.8

+2.4−2.4

+1.0−1.0

0.47 6.97 · 10−4 7 +54−25

+7.1−6.4

+1.1−0.4

−0.7+1.3

−3.3+4.2

+0.3−0.5

+3.7−3.7

+2.4−2.4

+2.7−2.7

0.61 6.75 · 10−4 8 +49−24

+9.4−9.9

+1.3−0.6

−1.1+3.0

−7.9+6.6

−0.5−0.1

+5.0−5.0

+2.4−2.4

+0.1−0.1

0.78 < 4.42 · 10−5 0

9055 0.16 5.35 · 10−3 16 +32−19

+6.5−12

+0.4−9.9

−4.6+3.8

+2.6−3.4

+0.6−1.4

+1.0−1.0

+2.4−2.4

+3.3−3.3

0.23 2.96 · 10−3 17 +31−19

+3.8−4.9

+1.3−1.7

−2.6+1.2

−1.9+1.2

−1.1+0.3

+0.4−0.4

+2.4−2.4

+1.0−1.0

0.33 1.23 · 10−3 12 +38−21

+4.0−4.5

+0.6−0.7

−2.2+1.6

−1.7+1.4

−0.3−0.1

+1.5−1.5

+2.4−2.4

+1.0−1.0

0.45 4.31 · 10−4 5 +67−27

+6.3−6.9

+0.4−0.7

−1.3+0.4

−4.2+3.4

+0.1−0.3

+3.4−3.4

+2.4−2.4

+2.7−2.7

0.59 2.12 · 10−4 3 +96−30

+9.8−7.0

+0.6−0.7

−1.4−0.4

−2.3+7.3

+0.1+0.3

+5.1−5.1

+2.4−2.4

+2.7−2.7

0.73 6.86 · 10−5 1 +220−30

+10−25

+1.1−6.2

−2.3−2.5

−23+8.3

−0.9+2.2

+4.6−4.6

+2.4−2.4

+0.1−0.1

0.90 < 8.12 · 10−6 0

14807 0.76 1.03 · 10−5 1 +220−30

+15−16

+2.1−2.6

−2.7+1.6

−15+14

−1.5+0.7

+2.5−2.5

+2.4−2.4

+0.1−0.1

0.92 < 1.28 · 10−6 0

17

Q2 xedge

∫ 1

xedged2σ/dxdQ2 N δs δt δu δ1 δ2 δ3 δ4 δ5 δ6

(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

648 0.25 8.49 · 10−2 34 +20−14

+8.5−6.7

+4.9−2.7

+6.1−5.2

+0.6+0.6

−0.8+1.1

+2.0−2.0

+1.6−1.6

+0.1−0.1

761 0.27 4.66 · 10−2 74 +13−10

+5.1−3.6

+1.8−1.1

+3.0−0.6

+0.9+0.9

−0.7+0.7

+2.5−2.5

+1.6−1.6

+0.1−0.1

891 0.30 3.19 · 10−2 109 +11−8.7

+6.5−3.7

+4.6−0.1

+2.2+0.5

+1.1+1.1

−1.0+1.1

+2.7−2.7

+1.6−1.6

+0.1−0.1

1045 0.32 2.08 · 10−2 101 +11−9.1

+6.9−5.8

+3.8−0.6

−4.4+4.2

+0.9+0.9

−1.0+0.7

+2.9−2.9

+1.6−1.6

+0.1−0.1

1224 0.35 1.03 · 10−2 65 +14−11

+6.0−3.9

+3.0−0.2

+0.6+3.2

+0.7+0.7

−0.4+0.7

+3.1−3.1

+1.6−1.6

+0.1−0.1

1431 0.38 5.65 · 10−3 42 +18−13

+7.2−6.0

+2.3−0.1

−4.3+5.3

+0.8+0.8

−1.1+0.7

+3.4−3.4

+1.6−1.6

+0.1−0.1

1672 0.41 3.66 · 10−3 29 +22−15

+5.8−4.6

+2.2−0.2

−1.3+2.8

+0.5+0.5

−0.7+1.5

+3.7−3.7

+1.6−1.6

+0.1−0.1

1951 0.44 2.07 · 10−3 21 +27−17

+6.8−5.5

+2.3−0.6

−2.5+4.1

+0.6+0.6

−1.1+1.0

+4.1−4.1

+1.6−1.6

+0.1−0.1

2273 0.48 1.22 · 10−3 13 +36−21

+7.3−8.3

+4.1−1.1

−5.7+2.9

+0.4+0.4

−2.9+0.9

+4.6−4.6

+1.6−1.6

+0.1−0.1

2644 0.52 2.87 · 10−4 4 +79−29

+8.7−6.8

+2.2−3.0

−2.1+6.5

+0.5+0.5

−2.3+0.9

+4.7−4.7

+1.6−1.6

+0.1−0.1

3073 0.56 < 8.32 · 10−5 0

3568 0.60 6.04 · 10−5 1 +220−30

+16−15

+4.5−3.1

−6.1+6.1

+1.4+1.4

−2.1+3.7

+4.7−4.7

+1.6−1.6

+13−13

4145 0.65 < 5.30 · 10−5 0

4806 0.70 < 5.79 · 10−5 0

5561 0.76 < 3.87 · 10−5 0

6966 0.89 < 1.61 · 10−6 0

Table 2: The integral cross section table for 96-97 e+p NC scattering. The first twocolumns of the table contain the Q2 and xedge values for the bin, the third contains

the measured cross section∫ 1

xedged2σ/dxdQ2 corrected to the electroweak Born level

or the upper limit in case of zero observed events, the fourth contains the numberof events reconstructed in the bin, N , the fifth contains the statistical uncertainty,δs, and the sixth contains the total systematic uncertainty, δt. The right part of thetable lists the total uncorrelated systematic uncertainty, δu, followed by the bin-to-bin correlated systematic uncertainties δ1– δ6 defined in the text. The upper (lower)numbers refer to the variation of the cross section, whereas the signs of the numbersreflect the direction of change in the cross sections. Note that the normalizationuncertainty, δ7 is not listed.

18


(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

648 0.08 2.76 51 +16−12

+8.3−9.0

+0.7−0.4

−7.0+5.6

−1.1+1.1

−3.0+3.6

+0.1−0.1

+2.4−2.4

+3.4−3.4

0.13 1.78 23 +25−17

+9.1−12

+3.6−3.3

−8.4+6.0

−1.3+0.1

−6.1+3.3

+0.0−0.0

+2.4−2.4

+3.4−3.4

0.19 8.63 · 10−1 14 +35−20

+11−15

+1.0−9.2

−9.2+8.8

−1.4+1.3

−5.4+4.3

+0.0+0.0

+2.4−2.4

+3.4−3.4

761 0.09 1.71 92 +12−9.4

+6.1−5.8

+1.0−1.4

−2.5+3.6

−0.9+0.8

−1.6+1.2

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.14 8.70 · 10−1 44 +17−13

+6.5−6.5

+1.1−1.1

−4.3+4.2

−0.4+0.3

−0.7+1.4

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.21 6.10 · 10−1 38 +19−14

+6.8−6.7

+1.3−1.1

−4.0+2.8

−1.4+2.8

−2.0+2.8

+0.0−0.0

+2.4−2.4

+3.3−3.3

891 0.10 1.36 137 +9.3−7.9

+4.8−4.7

+0.6−0.2

+0.0−0.4

−0.6+1.2

−0.2−0.1

+0.1−0.1

+2.4−2.4

+3.2−3.2

0.15 6.16 · 10−1 61 +15−11

+5.0−4.8

+0.5−0.2

−0.2+0.6

−1.4+0.2

+0.0+1.7

+0.1−0.1

+2.4−2.4

+3.2−3.2

0.22 5.20 · 10−1 68 +14−11

+5.5−5.3

+2.2−2.2

−1.3+1.7

+0.4+1.2

−0.2−0.2

+0.0+0.0

+2.4−2.4

+3.2−3.2

1045 0.07 1.56 148 +9.0−7.6

+4.9−5.2

+0.1−0.6

+1.9−2.4

+0.2+0.2

+0.8−1.1

+0.0−0.0

+2.4−2.4

+2.9−2.9

0.11 6.53 · 10−1 84 +12−9.7

+4.6−4.6

+0.3−0.4

+0.2−0.2

−1.3+1.3

+0.4−0.6

+0.1−0.1

+2.4−2.4

+2.9−2.9

0.17 4.61 · 10−1 67 +14−11

+4.6−4.8

+1.0−1.4

+1.0−0.2

−0.1−0.2

−0.6−1.2

+0.1−0.1

+2.4−2.4

+2.9−2.9

0.24 2.02 · 10−1 43 +18−13

+4.8−5.4

+1.1−0.9

+0.4−2.5

−1.5+1.4

−0.4+0.1

+0.1−0.1

+2.4−2.4

+2.9−2.9

1224 0.07 7.47 · 10−1 87 +12−9.6

+4.7−4.9

+0.3−1.1

+1.4−1.7

+0.0−0.4

+0.6−0.4

+0.0−0.0

+2.4−2.4

+2.9−2.9

0.12 4.90 · 10−1 80 +13−10

+4.7−4.7

+0.3−0.3

+0.9−1.5

−0.9+1.3

+0.5−0.1

+0.1−0.1

+2.4−2.4

+2.9−2.9

0.18 3.83 · 10−1 70 +13−11

+4.8−4.6

+1.5−0.2

−0.5−1.0

−0.9+0.3

+1.1+0.2

+0.1−0.1

+2.4−2.4

+2.9−2.9

0.26 1.63 · 10−1 44 +17−13

+5.1−4.9

+1.0−1.7

+0.5+0.0

−0.7+1.8

+1.6−1.0

+0.1−0.1

+2.4−2.4

+2.9−2.9

Table 3: The cross section table for 98-99 e−p NC scattering. The first twocolumns of the table contain the Q2 and x values at which the cross section isquoted, the third contains the measured cross section d2σ/dxdQ2 corrected to theelectroweak Born level or the upper limit in case of zero observed events, the fourthcontains the number of events reconstructed in the bin, N , the fifth contains thestatistical uncertainty, δs, and the sixth contains the total systematic uncertainty,δt. The right part of the table lists the total uncorrelated systematic uncertainty, δu,followed by the bin-to-bin correlated systematic uncertainties δ1– δ6 defined in thetext. The upper (lower) numbers refer to the variation of the cross section, whereasthe signs of the numbers reflect the direction of change in the cross sections. Notethat the normalization uncertainty, δ7 is not listed.

19



(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

1431 0.09 5.65 · 10−1 79 +13−10

+4.8−4.8

+0.3−0.7

+1.7−1.4

+0.6+0.3

+0.7−1.3

+0.1−0.1

+2.4−2.4

+2.8−2.8

0.14 2.69 · 10−1 55 +15−12

+4.6−4.9

+1.0−0.5

+0.9−1.9

−1.1+0.9

+0.4+0.0

+0.1−0.1

+2.4−2.4

+2.8−2.8

0.20 1.92 · 10−1 41 +18−13

+5.0−5.3

+1.1−0.7

+2.1−1.7

−1.3+0.7

+0.8−2.0

+0.0−0.0

+2.4−2.4

+2.8−2.8

0.29 1.29 · 10−1 41 +18−13

+4.8−4.7

+1.0−0.9

+0.9−1.5

−0.6+1.6

−0.1−0.1

+0.2−0.2

+2.4−2.4

+2.8−2.8

1672 0.10 3.25 · 10−1 57 +15−11

+4.3−4.2

+0.3−0.5

+1.2−0.7

−0.3−0.2

+0.4−0.2

+0.1−0.1

+2.4−2.4

+2.5−2.5

0.15 2.04 · 10−1 52 +16−12

+4.6−4.5

+0.4−0.5

+1.3−0.5

−1.2+1.6

+0.3−1.0

+0.1−0.1

+2.4−2.4

+2.5−2.5

0.22 1.03 · 10−1 28 +23−15

+4.2−4.6

+0.1−0.5

+0.9−1.6

−0.1−0.6

+0.3−0.8

+0.0−0.0

+2.4−2.4

+2.5−2.5

0.31 3.74 · 10−2 16 +32−20

+5.1−5.3

+1.2−1.5

+1.0−1.9

−2.0+2.5

+0.1−1.1

+0.3−0.3

+2.4−2.4

+2.5−2.5

1951 0.07 3.91 · 10−1 60 +15−11

+4.1−4.3

+0.3−0.7

+1.0−0.8

−1.1+0.5

+0.2−0.9

+0.0−0.0

+2.4−2.4

+2.2−2.2

0.11 1.86 · 10−1 39 +19−14

+4.9−4.4

+0.7−0.6

+2.4−1.3

+1.2−0.7

+0.7−1.0

+0.1−0.1

+2.4−2.4

+2.2−2.2

0.17 1.22 · 10−1 37 +19−14

+4.1−4.9

+0.2−2.7

+0.3+0.2

−1.2+0.5

+0.6+0.7

+0.1−0.1

+2.4−2.4

+2.2−2.2

0.24 7.22 · 10−2 26 +24−16

+5.0−4.5

+0.9−0.8

+2.6−0.4

−1.9+1.1

+0.2−0.6

+0.1−0.1

+2.4−2.4

+2.2−2.2

0.34 3.48 · 10−2 18 +30−19

+4.8−4.7

+1.8−1.8

−0.3−0.2

−1.1+1.9

−0.6−1.0

+0.4−0.4

+2.4−2.4

+2.2−2.2

2273 0.07 3.25 · 10−1 62 +14−11

+4.5−4.7

+0.5−1.2

+1.6−2.0

−0.9+0.2

+1.2−0.5

+0.0+0.0

+2.4−2.4

+2.2−2.2

0.12 1.19 · 10−1 31 +21−15

+4.2−4.8

+0.6−1.0

+0.7−2.4

+0.5−0.6

+0.9−0.5

+0.1−0.1

+2.4−2.4

+2.2−2.2

0.18 7.59 · 10−2 29 +22−15

+4.2−4.5

+0.3−0.9

+0.6−1.1

−1.6+1.3

+0.5−0.6

+0.1−0.1

+2.4−2.4

+2.2−2.2

0.26 5.21 · 10−2 23 +25−17

+4.6−4.5

+0.6−0.7

+0.7−1.9

−0.5+1.1

+1.8−0.2

+0.1−0.1

+2.4−2.4

+2.2−2.2

0.37 1.60 · 10−2 10 +43−23

+6.0−4.4

+2.5−0.8

+2.0−0.8

−1.6+2.5

+1.7−0.1

+0.5−0.5

+2.4−2.4

+2.2−2.2

2644 0.09 1.70 · 10−1 41 +18−13

+4.7−4.6

+0.6−1.8

+2.1−1.3

−0.9+0.8

+1.0−0.8

+0.1−0.1

+2.4−2.4

+2.1−2.1

0.14 7.79 · 10−2 29 +22−15

+4.2−4.5

+0.2−0.6

+1.4−1.7

+0.3+0.3

+0.7−1.2

+0.1−0.1

+2.4−2.4

+2.1−2.1

0.21 2.68 · 10−2 12 +38−21

+4.1−4.5

+0.4−0.2

+0.9−0.4

−2.1+0.7

+0.0+0.0

+0.0−0.0

+2.4−2.4

+2.1−2.1

0.29 3.26 · 10−2 19 +29−18

+4.9−4.1

+2.0−0.3

+1.0−0.9

+0.3+2.0

−0.5−0.8

+0.2−0.2

+2.4−2.4

+2.1−2.1

0.40 1.47 · 10−2 11 +40−22

+4.7−6.3

+1.1−2.1

+0.9−1.7

−3.9+2.2

+0.2−1.2

+0.5−0.5

+2.4−2.4

+2.1−2.1

3073 0.06 1.16 · 10−1 20 +28−18

+4.9−4.7

+0.4−1.3

+2.3−2.3

+1.3−0.3

+1.5−0.7

+0.1−0.1

+2.4−2.4

+2.0−2.0

0.10 9.39 · 10−2 25 +24−16

+4.1−5.8

+0.9−3.8

+0.8−1.5

−1.5+0.7

+0.1−0.4

+0.0−0.0

+2.4−2.4

+2.0−2.0

0.15 4.29 · 10−2 19 +29−18

+4.6−4.2

+0.6−0.4

+2.0−1.6

+0.4+0.1

+1.2−0.4

+0.1−0.1

+2.4−2.4

+2.0−2.0

0.23 2.53 · 10−2 14 +35−20

+7.7−4.9

+6.5−0.3

+0.6−1.6

−2.5+1.6

+0.3−0.8

+0.0−0.0

+2.4−2.4

+2.0−2.0

0.32 1.46 · 10−2 11 +40−22

+4.0−4.1

+0.4−0.6

+0.0−0.4

−1.3+0.1

+0.3+0.9

+0.2−0.2

+2.4−2.4

+2.0−2.0

0.43 9.60 · 10−4 1 +220−30

+6.8−4.5

+1.4−1.7

−0.8+0.0

−1.2+5.4

+0.4−0.4

+0.5−0.5

+2.4−2.4

+2.0−2.0

20



(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

3568 0.07 1.22 · 10−1 28 +23−15

+4.0−4.6

+0.9−1.2

+1.1−2.3

−0.0−0.2

+0.7−0.7

+0.0−0.0

+2.4−2.4

+1.7−1.7

0.11 3.80 · 10−2 14 +35−20

+4.1−8.2

+0.4−7.1

+0.9−1.4

+0.2+1.3

+0.5−0.8

+0.1−0.1

+2.4−2.4

+1.7−1.7

0.17 3.06 · 10−2 16 +32−19

+4.1−4.4

+0.2−0.7

+1.7−1.8

−0.9−0.1

+0.7−1.2

+0.1−0.1

+2.4−2.4

+1.7−1.7

0.25 2.37 · 10−2 17 +31−19

+4.7−4.2

+0.2−0.4

+1.5−1.3

−1.4+2.3

+1.1−0.5

+0.0−0.0

+2.4−2.4

+1.7−1.7

0.35 1.02 · 10−2 10 +43−23

+4.6−4.6

+1.9−0.9

+0.8−2.0

−0.9+1.7

+0.8−1.4

+0.3−0.3

+2.4−2.4

+1.7−1.7

0.47 8.33 · 10−4 1 +220−30

+7.5−5.7

+2.9−1.9

+3.7−2.5

−2.8+4.3

+1.2+0.1

+0.6−0.6

+2.4−2.4

+1.7−1.7

4145 0.08 5.23 · 10−2 15 +33−20

+7.8−4.0

+6.5−1.2

+2.0−0.6

+1.3−0.2

+0.6−0.9

+0.0−0.0

+2.4−2.4

+1.6−1.6

0.13 3.39 · 10−2 16 +32−19

+4.1−4.2

+0.3−0.8

+1.3−0.3

−1.8+1.1

+0.3−0.6

+0.1−0.1

+2.4−2.4

+1.6−1.6

0.19 1.88 · 10−2 13 +36−21

+4.0−4.2

+0.8−0.5

+1.3−1.6

−0.7+0.4

+0.2−0.9

+0.1−0.1

+2.4−2.4

+1.6−1.6

0.28 1.49 · 10−2 14 +35−20

+4.0−4.2

+0.3−0.6

+0.4−1.1

−1.3+1.4

+0.2−1.0

+0.1−0.1

+2.4−2.4

+1.6−1.6

0.39 3.33 · 10−3 4 +79−29

+5.6−3.8

+2.5−0.3

+1.8+0.0

−0.7+2.5

+0.6+1.3

+0.4−0.4

+2.4−2.4

+1.6−1.6

0.51 1.36 · 10−3 2 +130−32

+5.9−8.9

+3.3−2.6

+1.5−0.6

−6.2+2.9

−4.1−1.7

+0.7−0.7

+2.4−2.4

+1.6−1.6

4806 0.11 3.28 · 10−2 14 +35−20

+4.5−4.4

+0.2−0.7

+1.5−2.4

+1.1+1.1

+1.8−0.4

+0.0+0.0

+2.4−2.4

+1.4−1.4

0.16 1.70 · 10−2 10 +43−23

+4.5−4.5

+0.3−0.8

+0.6−1.2

−2.2+2.6

+0.9−0.9

+0.1−0.1

+2.4−2.4

+1.4−1.4

0.23 1.38 · 10−2 13 +36−21

+4.1−4.1

+0.6−0.3

+1.7+0.5

−1.6−0.6

+0.6−0.9

+0.0−0.0

+2.4−2.4

+1.4−1.4

0.33 5.78 · 10−3 7 +54−25

+4.1−5.2

+1.1−0.3

+1.3−2.2

−2.4+1.0

+0.4−1.8

+0.2−0.2

+2.4−2.4

+1.4−1.4

0.44 5.73 · 10−3 8 +49−24

+5.0−5.4

+1.2−2.8

+0.7−0.7

−2.6+3.2

+0.2−1.2

+0.4−0.4

+2.4−2.4

+1.4−1.4

0.56 1.23 · 10−3 2 +130−32

+7.8−12

+4.3−1.1

−3.2−3.9

−9.8+3.3

+4.3+0.1

+0.4−0.4

+2.4−2.4

+1.4−1.4

5561 0.12 1.90 · 10−2 10 +43−24

+4.1−4.5

+0.2−1.3

+1.8−1.2

−1.7−0.5

+1.2−1.4

+0.0−0.0

+2.4−2.4

+1.2−1.2

0.18 1.03 · 10−2 8 +49−24

+5.8−3.7

+0.3−0.4

+0.8−1.1

+1.0+4.5

+0.1−0.1

+0.1−0.1

+2.4−2.4

+1.2−1.2

0.26 4.73 · 10−3 6 +60−26

+4.0−4.0

+0.5−0.3

+1.2−1.2

−1.5+1.5

+0.0−0.4

+0.1−0.1

+2.4−2.4

+1.2−1.2

0.37 6.69 · 10−4 1 +220−30

+4.2−4.3

+1.2−0.6

+0.8−0.4

−2.4+1.3

+0.6+0.8

+0.3−0.3

+2.4−2.4

+1.2−1.2

0.49 1.70 · 10−3 3 +96−30

+5.6−7.2

+1.7−3.5

−2.1−4.0

−2.4+3.9

+0.9−0.5

+0.6−0.6

+2.4−2.4

+1.2−1.2

0.61 < 6.44 · 10−4 0

6966 0.14 1.37 · 10−2 22 +26−17

+4.1−5.2

+0.9−3.1

+1.8−2.1

−0.9+0.1

+0.8−0.7

+0.0−0.0

+2.4−2.4

+1.0−1.0

0.21 6.68 · 10−3 14 +35−20

+4.1−4.2

+0.4−0.8

+1.5−1.5

−1.8+1.3

+0.7−0.5

+0.0−0.0

+2.4−2.4

+1.0−1.0

0.30 2.06 · 10−3 7 +54−25

+4.6−4.1

+0.3−0.5

+1.8−0.9

−2.0+2.3

+0.7−0.6

+0.2−0.2

+2.4−2.4

+1.0−1.0

0.41 1.87 · 10−3 7 +54−25

+4.7−4.4

+0.8−0.3

+1.7−0.8

−2.4+2.5

+0.6−0.8

+0.4−0.4

+2.4−2.4

+1.0−1.0

0.53 2.14 · 10−4 1 +220−30

+6.1−4.9

+0.3−0.7

+1.6−0.8

−3.2+4.7

+0.6−1.0

+0.5−0.5

+2.4−2.4

+1.0−1.0

21



(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

0.69 1.17 · 10−4 1 +220−30

+18−17

+14−15

+4.2+4.5

−7.0+9.5

−0.5−1.4

+0.6−0.6

+2.4−2.4

+1.0−1.0

9059 0.13 5.13 · 10−3 4 +79−29

+8.1−23

+0.9−22

+2.8−3.4

+6.6−2.8

+1.7−1.5

+0.0−0.0

+2.4−2.4

+0.7−0.7

0.19 3.64 · 10−3 8 +49−24

+4.4−5.0

+0.7−2.1

+2.3−2.5

−1.0+1.1

+1.1−1.5

+0.1−0.1

+2.4−2.4

+0.7−0.7

0.27 3.10 · 10−3 11 +40−22

+4.0−4.3

+0.5−1.0

+1.1−1.6

−1.8+1.8

+0.6−0.7

+0.1−0.1

+2.4−2.4

+0.7−0.7

0.38 3.84 · 10−4 2 +130−32

+4.5−5.7

+0.8−0.6

+0.8+0.3

−4.5+2.7

+0.5−0.3

+0.4−0.4

+2.4−2.4

+0.7−0.7

0.51 1.73 · 10−4 1 +220−30

+5.5−4.9

+1.5−1.2

+1.2−1.0

−3.1+3.8

+0.6−0.7

+0.6−0.6

+2.4−2.4

+0.7−0.7

0.64 < 1.83 · 10−4 0

0.78 9.12 · 10−5 1 +220−30

+9.9−13

+1.8−1.1

+1.0−1.6

−12+8.8

+0.4−0.3

+2.2−2.2

+2.4−2.4

+0.7−0.7

0.93 < 1.08 · 10−5 0

15072 0.61 8.57 · 10−5 3 +96−30

+22−25

+18−20

−5.9−9.5

−8.9+11

+0.4−1.1

+0.9−0.9

+2.4−2.4

+0.5−0.5

0.75 < 1.97 · 10−5 0

0.91 < 2.04 · 10−6 0

22

Q2 xedge

∫ 1


(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

648 0.22 8.74 · 10−2 14 +35−20

+8.7−8.2

+3.7−1.9

−5.9+5.6

+0.0+0.0

−3.0+3.4

+0.3−0.3

+1.6−1.6

+3.4−3.4

761 0.24 7.12 · 10−2 54 +16−12

+5.5−6.0

+0.5−0.5

−3.7+2.7

+0.0−0.1

−1.9+2.1

+0.2−0.2

+1.6−1.6

+3.3−3.3

891 0.26 3.44 · 10−2 56 +15−12

+4.5−4.4

+1.3−0.6

+0.3−0.6

+0.0−0.1

+0.6−0.6

+0.2−0.2

+1.6−1.6

+3.2−3.2

1045 0.29 2.29 · 10−2 54 +16−12

+4.5−4.5

+1.3−0.9

+1.5−1.5

+0.0−0.2

+0.7−1.0

+0.3−0.3

+1.6−1.6

+2.9−2.9

1224 0.31 9.38 · 10−3 28 +23−15

+4.9−5.5

+0.2−0.5

+2.4−3.6

−0.2−0.2

+1.4−1.1

+0.2−0.2

+1.6−1.6

+2.9−2.9

1431 0.34 8.51 · 10−3 29 +22−15

+5.4−5.5

+0.2−0.1

+3.6−2.9

+0.3+0.2

+0.6−2.4

+0.2−0.2

+1.6−1.6

+2.8−2.8

1672 0.36 6.31 · 10−3 25 +24−16

+4.4−4.5

+0.8−0.3

+1.4−1.9

−0.4−0.5

+1.7−1.6

+0.2−0.2

+1.6−1.6

+2.5−2.5

1951 0.39 3.34 · 10−3 16 +32−19

+6.9−4.3

+1.8−1.6

+5.1−1.6

+1.1+1.0

+2.0−0.9

+0.2−0.2

+1.6−1.6

+2.2−2.2

2273 0.43 1.61 · 10−3 8 +49−24

+5.6−7.5

+3.1−2.0

+2.9−5.4

−0.5−0.5

+1.0−3.1

+0.2−0.2

+1.6−1.6

+2.2−2.2

2644 0.46 8.11 · 10−4 5 +67−27

+6.3−5.6

+2.1−0.2

+3.9−4.0

+1.4+1.4

+1.9−1.8

+0.2−0.2

+1.6−1.6

+2.1−2.1

3073 0.50 < 1.62 · 10−4 0

3568 0.54 2.43 · 10−4 2 +130−32

+7.6−4.5

+3.3−0.5

+5.3−2.5

+1.1+0.8

+2.5−1.9

+0.2−0.2

+1.6−1.6

+1.7−1.7

4145 0.58 2.06 · 10−4 2 +130−32

+6.2−4.6

+0.7−0.7

+3.6−1.7

+0.1+0.1

+3.9−2.8

+0.1−0.1

+1.6−1.6

+1.6−1.6

4806 0.63 < 1.02 · 10−4 0

5561 0.68 < 8.95 · 10−5 0

6966 0.79 < 1.38 · 10−5 0

Table 4: The integral cross section table for 98-99 e−p NC scattering. The first twocolumns of the table contain the Q2 and xedge values for the bin, the third contains




23


(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

648 0.08 3.02 255 +6.6−5.9

+7.8−7.1

+1.3−1.0

+5.8−5.2

−0.9+1.8

+0.2−0.3

+0.3−0.3

+2.4−2.4

+3.3−3.3

0.13 1.86 116 +10−8.4

+7.5−7.5

+2.1−1.3

+5.2−5.6

−1.0+0.6

+1.8+0.3

+0.2−0.2

+2.4−2.4

+3.3−3.3

0.19 1.05 87 +11−9.6

+11−9.7

+4.7−3.4

+8.6−7.4

−1.2+1.8

+1.0−2.3

+0.1−0.1

+2.4−2.4

+3.3−3.3

761 0.09 1.85 403 +5.2−4.7

+5.2−5.5

+0.4−0.9

+2.1−2.6

−0.6+0.7

+0.0+0.1

+0.2−0.2

+2.4−2.4

+3.3−3.3

0.14 9.89 · 10−1 216 +7.3−6.3

+6.0−5.2

+0.6−1.2

+3.6−2.0

−0.7+0.9

+0.9−0.2

+0.0−0.0

+2.4−2.4

+3.3−3.3

0.21 6.18 · 10−1 161 +8.5−7.3

+4.9−5.4

+1.0−0.7

+1.9−3.1

−1.4+1.8

+2.0−2.4

+0.2−0.2

+2.4−2.4

+1.0−1.0

891 0.10 1.23 471 +4.8−4.4

+4.7−4.9

+0.3−1.1

+0.5−1.0

−0.7+0.2

+0.3−0.2

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.15 7.65 · 10−1 301 +6.1−5.4

+5.1−4.9

+1.6−0.4

−0.6+0.1

−0.7+1.1

+0.7−1.1

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.22 3.64 · 10−1 189 +7.9−6.8

+4.9−4.3

+2.2−0.3

+2.4−1.5

−1.7+1.1

+0.9−1.1

+0.2−0.2

+2.4−2.4

+1.0−1.0

1045 0.07 1.49 532 +4.5−4.2

+5.5−5.2

+0.7−0.6

−2.3+2.9

−0.1+0.2

−0.6+0.6

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.11 7.98 · 10−1 388 +5.3−4.8

+4.9−4.9

+0.9−0.1

−0.2+0.8

−1.4+1.0

+0.0−0.3

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.17 4.82 · 10−1 253 +6.7−5.9

+4.9−4.8

+0.9−0.7

+0.1+0.5

−0.1+0.1

+1.3−1.1

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.24 2.21 · 10−1 173 +8.2−7.1

+4.3−4.5

+0.6−1.1

−2.0+1.9

−0.8+1.1

+1.3−1.6

+0.2−0.2

+2.4−2.4

+1.0−1.0

1224 0.07 1.03 444 +5.0−4.5

+4.9−5.0

+0.8−0.2

−1.7+1.4

−0.1+0.1

−0.4+0.4

+0.2−0.2

+2.4−2.4

+3.3−3.3

0.12 4.81 · 10−1 294 +6.2−5.5

+4.9−5.1

+0.4−0.9

−1.7+1.6

−0.7+0.1

−0.1−0.3

+0.0−0.0

+2.4−2.4

+3.3−3.3

0.18 2.99 · 10−1 208 +7.4−6.4

+4.8−5.0

+0.5−0.5

−0.8+0.7

−1.0+0.1

+0.9−1.4

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.26 1.31 · 10−1 139 +9.2−7.8

+5.3−3.8

+0.4−0.6

−0.9+0.9

−0.2+1.9

+3.4−1.2

+0.1−0.1

+2.4−2.4

+1.0−1.0

Table 5: The cross section table for 99-00 e+p NC scattering. The first twocolumns of the table contain the Q2 and x values at which the cross section isquoted, the third contains the measured cross section d2σ/dxdQ2 corrected to theelectroweak Born level or the upper limit in case of zero observed events, the fourthcontains the number of events reconstructed in the bin, N , the fifth contains thestatistical uncertainty, δs, and the sixth contains the total systematic uncertainty,δt. The right part of the table lists the total uncorrelated systematic uncertainty, δu,followed by the bin-to-bin correlated systematic uncertainties δ1– δ6 defined in thetext. The upper (lower) numbers refer to the variation of the cross section, whereasthe signs of the numbers reflect the direction of change in the cross sections. Notethat the normalization uncertainty, δ7 is not listed.

24



(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

1431 0.09 5.29 · 10−1 278 +6.4−5.6

+5.0−4.7

+0.5−0.3

−0.4+1.7

−0.0−0.4

−0.2+0.2

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.14 2.74 · 10−1 212 +7.3−6.4

+5.0−4.8

+0.6−0.3

−0.8+0.9

−0.9+1.4

−0.0−0.1

+0.0−0.0

+2.4−2.4

+3.3−3.3

0.20 1.51 · 10−1 126 +9.7−8.1

+3.8−4.3

+0.8−1.2

−1.4+0.9

−0.6+0.4

+1.0−1.7

+0.2−0.2

+2.4−2.4

+1.0−1.0

0.29 0.99 · 10−1 119 +10−8.3

+5.2−4.5

+1.9−0.1

−0.2+2.2

−1.8+1.5

+2.2−2.1

+0.0−0.0

+2.4−2.4

+1.0−1.0

1672 0.10 3.71 · 10−1 249 +6.8−6.0

+4.9−5.0

+0.6−0.6

−1.6+1.5

−0.1+0.3

−0.2+0.2

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.15 1.93 · 10−1 183 +8.0−6.9

+4.8−4.9

+0.5−0.7

−1.1+1.1

−0.7+0.7

+0.2−0.1

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.22 1.05 · 10−1 113 +10−8.6

+3.7−4.1

+0.2−0.8

−1.3+0.8

−0.3+0.1

+1.0−1.4

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.31 6.10 · 10−2 96 +11−9.2

+5.0−4.2

+1.0−0.3

−0.6+0.6

−2.1+2.9

+1.7−0.7

+0.1−0.1

+2.4−2.4

+1.0−1.0

1951 0.07 3.77 · 10−1 215 +7.3−6.3

+4.9−4.9

+0.6−0.4

−1.5+1.1

−0.0+0.6

+0.1−0.1

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.11 1.89 · 10−1 149 +8.9−7.5

+5.1−5.1

+0.6−0.9

−1.8+2.0

−0.3−0.6

−0.3+0.2

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.17 1.10 · 10−1 126 +9.7−8.1

+5.2−4.9

+1.2−0.4

−1.0+1.0

−1.2+1.6

+0.5−0.4

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.24 7.26 · 10−2 102 +11−9.0

+4.2−3.7

+1.1−0.3

−0.8+1.9

−0.5+0.2

+0.9−0.9

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.34 3.34 · 10−2 69 +14−11

+4.7−4.2

+0.2−1.0

−1.2+0.8

−1.7+2.6

+1.7−0.9

+0.2−0.2

+2.4−2.4

+1.0−1.0

2273 0.07 2.41 · 10−1 179 +8.1−7.0

+5.1−5.0

+0.9−0.4

−1.4+1.7

−1.0+0.8

−0.0−0.0

+0.2−0.2

+2.4−2.4

+3.3−3.3

0.12 1.55 · 10−1 150 +8.8−7.5

+5.1−5.1

+0.6−1.0

−1.7+2.0

−0.4−0.2

−0.5+0.4

+0.0−0.0

+2.4−2.4

+3.3−3.3

0.18 8.25 · 10−2 114 +10−8.5

+5.1−4.9

+0.2−0.6

−0.6+1.3

−1.4+1.5

+0.2−0.3

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.26 3.77 · 10−2 68 +14−11

+4.3−3.7

+1.0−0.2

−0.7+1.8

+0.7+0.4

+1.0−1.1

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.37 1.71 · 10−2 40 +19−13

+5.1−4.9

+0.8−0.3

−1.4+2.3

−2.8+2.2

+1.9−1.4

+0.3−0.3

+2.4−2.4

+1.0−1.0

2644 0.09 1.48 · 10−1 135 +9.4−7.9

+5.2−5.1

+0.5−0.5

−1.3+1.8

−1.5+1.4

−0.3+0.3

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.14 7.74 · 10−2 107 +11−8.8

+4.9−5.1

+0.5−0.6

−2.1+1.6

−0.1+0.1

+0.1−0.0

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.21 4.65 · 10−2 77 +13−10

+4.3−4.0

+1.5−0.6

−2.0+0.8

−0.4+1.9

+0.2−0.2

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.29 2.58 · 10−2 57 +15−11

+3.7−4.6

+0.0−1.8

−1.6+0.1

−1.1+0.7

+1.2−1.4

+0.0−0.0

+2.4−2.4

+1.0−1.0

0.40 1.11 · 10−2 33 +21−15

+5.1−5.6

+0.6−0.5

−0.0+0.0

−3.3+2.4

+1.2−1.3

+0.4−0.4

+2.4−2.4

+2.7−2.7

3073 0.06 1.24 · 10−1 83 +12−9.8

+5.1−5.3

+0.3−0.6

−2.4+1.9

+0.8−0.0

+0.4−0.3

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.10 8.34 · 10−2 87 +11−9.7

+5.2−4.8

+1.2−0.8

−0.9+1.7

−0.4+0.8

−0.4+0.2

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.15 5.79 · 10−2 99 +11−9.0

+4.9−4.7

+0.5−0.3

−0.7+1.3

−0.5−0.4

−0.2+0.1

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.23 2.52 · 10−2 53 +16−12

+3.9−3.8

+0.8−0.2

−0.6+1.1

−1.4+0.9

+0.6−0.4

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.32 1.79 · 10−2 49 +16−12

+4.7−4.4

+0.2−0.9

−2.2+1.7

−1.0+2.6

+0.7−0.7

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.43 5.58 · 10−3 21 +27−17

+5.5−5.4

+0.2−0.6

−1.0+1.2

−2.9+2.9

+1.2−1.3

+0.5−0.5

+2.4−2.4

+2.7−2.7

25



(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

3568 0.07 6.73 · 10−2 59 +15−11

+5.2−5.3

+1.4−0.9

−2.2+1.7

+0.6−0.7

+0.3−0.3

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.11 4.68 · 10−2 64 +14−11

+4.9−5.4

+0.3−1.2

−2.3+1.5

−0.8+0.6

−0.1+0.2

+0.0−0.0

+2.4−2.4

+3.3−3.3

0.17 3.15 · 10−2 62 +14−11

+4.8−5.3

+0.7−0.2

−2.4+1.2

+0.1−0.7

−0.2+0.1

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.25 2.06 · 10−2 56 +15−12

+4.1−4.4

+0.3−0.6

−1.6+1.0

−2.1+1.9

+0.5−0.2

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.35 8.84 · 10−3 33 +21−15

+4.3−3.7

+1.5−0.4

−0.7−0.0

−0.9+1.9

+0.6−0.7

+0.2−0.2

+2.4−2.4

+1.0−1.0

0.47 4.14 · 10−3 19 +29−18

+6.1−5.4

+0.7−0.4

−0.5+1.3

−3.1+3.6

+1.8−0.6

+0.6−0.6

+2.4−2.4

+2.7−2.7

4145 0.08 5.56 · 10−2 58 +15−11

+6.3−5.3

+1.8−1.0

−2.3+3.4

+1.6−0.6

+0.5−0.5

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.13 3.04 · 10−2 53 +16−12

+5.4−4.9

+0.8−0.4

−1.2+2.5

−0.7+0.4

−0.3+0.5

+0.0−0.0

+2.4−2.4

+3.3−3.3

0.19 1.74 · 10−2 47 +17−13

+4.8−4.9

+0.3−0.6

−1.3+0.8

−0.5+1.0

+0.1+0.1

+0.2−0.2

+2.4−2.4

+3.3−3.3

0.28 1.05 · 10−2 36 +20−14

+5.4−4.1

+3.0−0.7

−1.3+2.1

−1.6+1.9

+0.1−0.6

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.39 5.24 · 10−3 23 +25−17

+4.0−4.4

+0.6−1.3

−1.3+0.0

−1.8+1.7

+0.8−0.9

+0.3−0.3

+2.4−2.4

+1.0−1.0

0.51 1.21 · 10−3 7 +54−25

+6.1−6.8

+1.2−0.9

−2.4+2.2

−4.5+3.2

+1.4−0.6

+0.5−0.5

+2.4−2.4

+2.7−2.7

4806 0.11 2.12 · 10−2 33 +21−15

+4.9−5.3

+0.3−2.0

−1.6+1.1

+0.4+0.7

+0.1−0.4

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.16 2.12 · 10−2 47 +17−13

+5.0−5.3

+0.7−2.2

−1.1+1.3

−0.7+1.2

−0.4+0.6

+0.1−0.1

+2.4−2.4

+3.3−3.3

0.23 8.94 · 10−3 30 +22−15

+3.8−3.9

+0.2−0.2

−1.5+1.6

−1.0−0.2

+0.3+0.1

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.33 5.20 · 10−3 23 +25−17

+4.6−4.1

+1.3−0.3

+0.8+1.2

−2.2+2.3

+0.1−0.6

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.44 1.88 · 10−3 10 +43−23

+5.2−6.0

+0.5−1.3

−1.2+0.8

−3.6+2.8

+0.6−1.3

+0.4−0.4

+2.4−2.4

+2.7−2.7

0.56 6.34 · 10−4 4 +79−29

+7.6−5.5

+2.0−1.0

+1.1+1.9

−3.2+5.0

+0.2+2.3

+0.4−0.4

+2.4−2.4

+2.7−2.7

5561 0.12 1.44 · 10−2 30 +22−15

+5.0−5.5

+0.5−2.4

−1.3+1.9

−0.8−0.4

+0.3+0.0

+0.0−0.0

+2.4−2.4

+3.3−3.3

0.18 8.24 · 10−3 24 +25−17

+5.7−5.1

+0.7−0.5

−1.8+2.8

−0.6+1.6

−0.7+0.6

+0.2−0.2

+2.4−2.4

+3.3−3.3

0.26 5.46 · 10−3 25 +24−16

+4.6−4.4

+0.7−0.6

−2.3+2.8

−1.3+1.1

+0.3−0.1

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.37 2.41 · 10−3 13 +36−21

+3.8−4.1

+0.3−0.4

−0.5+0.2

−2.1+1.6

+0.1−0.4

+0.2−0.2

+2.4−2.4

+1.0−1.0

0.49 7.28 · 10−4 5 +67−27

+7.0−6.0

+1.0−0.5

−1.9+3.6

−3.7+3.9

+1.2+0.2

+0.5−0.5

+2.4−2.4

+2.7−2.7

0.61 < 1.52 · 10−4 0

6966 0.14 6.39 · 10−3 39 +19−14

+5.7−5.3

+2.1−1.1

−2.4+2.6

+0.3−0.2

+0.2−0.1

+0.0−0.0

+2.4−2.4

+3.3−3.3

0.21 6.94 · 10−3 53 +16−12

+4.1−4.0

+0.7−0.3

−1.6+1.7

−1.1+1.3

−0.5+0.5

+0.2−0.2

+2.4−2.4

+1.0−1.0

0.30 1.94 · 10−3 24 +25−17

+4.0−4.1

+0.5−0.1

−1.1+1.2

−1.9+1.5

−0.1+0.0

+0.1−0.1

+2.4−2.4

+1.0−1.0

0.41 1.10 · 10−3 16 +32−20

+5.1−5.0

+0.5−0.3

−1.0+1.4

−2.2+2.3

+0.4−0.4

+0.2−0.2

+2.4−2.4

+2.7−2.7

0.53 3.39 · 10−4 6 +60−26

+6.7−6.1

+0.7−0.7

−1.1+1.0

−4.1+4.9

+0.8−0.2

+0.5−0.5

+2.4−2.4

+2.7−2.7

26



(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

0.66 4.49 · 10−5 1 +220−30

+9.8−7.8

+1.0−0.9

−0.9+0.8

−6.4+8.6

−2.7+3.1

+0.7−0.7

+2.4−2.4

+0.1−0.1

9059 0.13 3.71 · 10−3 11 +40−22

+8.3−9.4

+0.3−5.5

−3.5+4.1

+5.4−4.8

+0.5−0.9

+0.5−0.5

+2.4−2.4

+3.3−3.3

0.19 3.48 · 10−3 28 +23−15

+5.9−5.7

+1.8−0.6

−3.2+3.2

−0.4+0.4

+0.1+0.3

+0.2−0.2

+2.4−2.4

+3.3−3.3

0.27 1.73 · 10−3 22 +26−17

+4.1−4.5

+0.7−0.3

−2.8+1.8

−0.7+1.0

−0.4+0.1

+0.2−0.2

+2.4−2.4

+1.0−1.0

0.38 8.34 · 10−4 16 +32−19

+5.0−4.9

+0.5−0.3

−1.3+1.2

−3.2+3.3

+0.1+0.2

+0.2−0.2

+2.4−2.4

+1.0−1.0

0.51 1.47 · 10−4 3 +96−30

+6.2−5.5

+0.7−0.1

−0.9+1.7

−3.2+4.0

+0.5−0.7

+0.4−0.4

+2.4−2.4

+2.7−2.7

0.64 8.16 · 10−5 2 +130−32

+6.5−7.0

+1.2−0.5

−1.8+2.2

−5.8+5.1

−0.4+0.1

+0.0−0.0

+2.4−2.4

+0.1−0.1

0.78 < 2.25 · 10−5 0

0.93 < 4.38 · 10−6 0

15072 0.61 3.58 · 10−5 4 +79−29

+6.3−7.8

+2.3−0.9

−2.0+1.5

−6.7+4.5

−0.1+0.3

+0.3−0.3

+2.4−2.4

+0.1−0.1

0.75 4.98 · 10−6 1 +220−30

+26−6.8

+2.7−0.7

−1.0+2.0

−5.7+25

−0.4+0.2

+1.2−1.2

+2.4−2.4

+0.1−0.1

0.91 < 7.42 · 10−7 0

27

Q2 xedge

∫ 1


(GeV2) (pb/GeV2) (%) (%) (%) (%) (%) (%) (%) (%) (%)

648 0.22 1.33 · 10−1 106 +11−8.8

+9.8−4.4

+2.4−2.3

+9.0−2.4

+0.2+0.0

−0.6+1.4

+0.1−0.1

+1.6−1.6

+0.1−0.1

761 0.24 6.73 · 10−2 212 +7.3−6.4

+3.8−5.2

+2.0−3.0

+1.7−3.2

+0.1+0.0

−0.1+0.4

+0.0−0.0

+1.6−1.6

+0.1−0.1

891 0.26 4.41 · 10−2 288 +6.2−5.5

+3.3−3.3

+1.0−1.0

−1.4+1.6

+0.0+0.0

−0.9+0.3

+0.1−0.1

+1.6−1.6

+0.1−0.1

1045 0.29 2.50 · 10−2 224 +7.1−6.3

+4.1−3.3

+1.2−0.7

−1.6+2.7

+0.1+0.0

−0.4+0.3

+0.1−0.1

+1.6−1.6

+0.1−0.1

1224 0.31 1.48 · 10−2 157 +8.6−7.3

+3.7−4.2

+1.7−1.0

−3.0+1.5

+0.1+0.0

−0.5+1.1

+0.1−0.1

+1.6−1.6

+0.1−0.1

1431 0.34 9.52 · 10−3 120 +10−8.3

+4.0−3.7

+0.3−0.4

−2.3+2.7

+0.0−0.0

−0.8+0.9

+0.1−0.1

+1.6−1.6

+0.1−0.1

1672 0.36 3.90 · 10−3 59 +15−11

+4.6−4.5

+0.2−0.7

−3.4+3.3

+0.0+0.0

−0.7+1.4

+0.2−0.2

+1.6−1.6

+0.1−0.1

1951 0.39 2.64 · 10−3 46 +17−13

+4.9−4.7

+0.9−1.0

−3.5+3.8

+0.0+0.0

−1.0+1.2

+0.2−0.2

+1.6−1.6

+0.1−0.1

2273 0.43 1.52 · 10−3 29 +22−15

+4.8−4.3

+0.6−0.7

−3.0+3.7

+0.0+0.0

−1.2+1.0

+0.1−0.1

+1.6−1.6

+0.1−0.1

2644 0.46 9.16 · 10−4 22 +26−17

+4.2−4.8

+1.4−1.4

−3.6+2.4

+0.0+0.0

−0.9+1.5

+0.2−0.2

+1.6−1.6

+0.1−0.1

3073 0.50 4.79 · 10−4 13 +36−21

+6.5−7.2

+0.7−0.3

−6.6+5.8

+0.0+0.0

−0.6+0.9

+0.1−0.1

+1.6−1.6

+0.1−0.1

3568 0.54 2.27 · 10−4 7 +54−25

+4.8−7.0

+1.1−2.0

−5.8+3.6

+0.0+0.0

−2.0+1.1

+0.1−0.1

+1.6−1.6

+0.1−0.1

4145 0.58 7.57 · 10−5 3 +96−30

+6.6−6.4

+1.3−2.2

−4.8+5.4

+0.0+0.0

−2.4+2.3

+0.0−0.0

+1.6−1.6

+0.1−0.1

4806 0.63 7.05 · 10−5 3 +96−30

+15−15

+5.4−2.1

−7.1+6.5

+0.0+0.0

−3.6+1.6

+0.2−0.2

+1.6−1.6

+13−13

5561 0.68 6.09 · 10−5 3 +96−30

+14−14

+1.2−3.4

−4.4+5.3

+0.0−0.1

−1.6+3.5

+0.3−0.3

+1.6−1.6

+13−13

6966 0.79 < 4.07 · 10−6 0

Table 6: The integral cross section table for 99-00 e+p NC scattering. The first twocolumns of the table contain the Q2 and xedge values for the bin, the third contains




28

Figure 1: A schematic depiction of the ZEUS detector with the main componentsused in this analysis labeled. Also shown is a typical topology for events studied inthis analysis. The electron is scattered at a large angle and is reconstructed usingthe central tracking detector (CTD) and the barrel calorimeter (BCAL), while thescattered jet is typically reconstructed in the forward calorimeter (FCAL). The jetof particles from the proton remnant mostly disappears down the beam pipe.

29

ZEUS

(cm)vtxZ-40 -20 0 20 40

Eve

nts

10

210

310

p+ZEUS NC 99-00 eCTEQ6D NC MC

(a)

(GeV)δ40 50 60 70

Eve

nts

1

10

210

310(b)

)GeV (TE/TP0 1 2 3 4

Eve

nts

-110

1

10

210

310(c)

)2 (GeV2Q2000 4000 6000

Eve

nts

10

210

310

410 (d)

Figure 2: Comparison of NC MC distributions (histograms) with 99-00 e+p data(points) for: (a) the Z coordinate of the event vertex; (b) δ; (c) PT/

√ET and (d)

Q2. The MC distributions are normalized to the measured luminosity.

30

ZEUS

(GeV)eE’100 200 300

Eve

nts

-110

110

210

310

410

(GeV)eE’100 200 300

Eve

nts

-110

110

210

310

410p+ZEUS NC 99-00 e

CTEQ6D NC MC

(a)

(rad)eθ0 0.5 1 1.5 2

Eve

nts

1

10

210

310

(rad)eθ0 0.5 1 1.5 2

Eve

nts

1

10

210

310(b)

(rad)e

φ-2 0 2

Eve

nts

0

500

1000

1500

2000

(rad)e

φ-2 0 2

Eve

nts

0

500

1000

1500

2000(c)

(GeV)trk

p100 200 300

Eve

nts

1

10

210

310

410

(GeV)trk

p100 200 300

Eve

nts

1

10

210

310

410 (d)

Figure 3: Comparison of NC MC distributions (histograms) with 99-00 e+pdata (points) for: (a) E ′

e; (b) θe; (c) φe and (d) ptrk, the momentum of the trackassociated with the scattered electron. The MC distributions are normalized to themeasured luminosity.

31

ZEUS

jetsN0 1 2 3 4

Eve

nts

1

10

210

310

410 (a)

(GeV)jetE200 400 600

Eve

nts

1

10

210

310(b)

(rad)jetθ0 1 2 3

Eve

nts

-110

1

10

210

310(c)

(rad)jet

φ0 2 4 6

Eve

nts

0

500

1000

1500

2000 (d)

x0 0.2 0.4 0.6 0.8 1

Eve

nts

-110

1

10

210

310(e)

p+ZEUS NC 99-00 e

CTEQ6D NC MC

Figure 4: Comparison of NC MC distributions (histograms) with 99-00 e+p data(points) for: (a) the number of reconstructed jets; (b) Ejet; (c) θjet; (d) φjet and(e) x calculated from the jet. The jet distributions are for one jet events. The MCdistributions are normalized to the measured luminosity.

32

ZEUS

(cm)vtxZ-40 -20 0 20 40

Eve

nts

0

50

100(a)

(GeV)δ50 55 60 65

Eve

nts

0

50

100

150

200(b)

(GeV)eE’40 60 80 100 120

Eve

nts

-110

1

10

210(c)

(rad)eθ0 0.5 1 1.5 2

Eve

nts

-110

1

10

210

310 (d)

(rad)e

φ-2 0 2

Eve

nts

0

50

100

150(e)

Zero-jet samplep+ZEUS NC 99-00 e

CTEQ6D NC MC

Figure 5: Comparison of NC MC distributions (histograms) with 99-00 e+p data(points) for events with zero jets. The plots show: (a) the Z coordinate of the eventvertex; (b) δ; (c) E ′

e; (d) θe and (e) φe. The MC distributions are normalized tothe measured luminosity.

33

x0.2 0.4 0.6 0.8 1

)2 (

GeV

2Q

310

410

y=1

=0.12

jetθ

(a)

98-00

x0.2 0.4 0.6 0.8 1

)2 (

GeV

2Q

310

410

y=1

=0.12jetθ

(b)

96-97

Figure 6: Definition of the bins as used in this analysis for: (a) 98-00 datawith Ep = 920 GeV and (b) 96-97 data with Ep = 820 GeV . The shaded binsextending to x = 1 are for the zero-jet events. The y = 1 lines shows the kinematiclimit. The θjet = 0.12 rad shows the selection cut for jets.

34

ZEUS

truex

Eve

nts

0 0.2 0.4 0.6 0.8 10

20

40

2< 961GeV2 821<Q

zero-jet MCedgex

0 0.2 0.4 0.6 0.8 10

1

22<3302GeV22843<Q

0 0.2 0.4 0.6 0.8 10

5

10

15

2<1801GeV21542<Q

0 0.2 0.4 0.6 0.8 10

0.1

2<5965GeV25157<Q

Figure 7: The true x distribution for zero-jet events from 99-00 e+p MC simu-lations in different Q2 bins. The dashed lines represent the lower edge of the bins,xedge. The MC distributions are normalized to the luminosity of the data.

35

ZEUS

x

)2 (

GeV

2Q

310

410

11 6.9 5.5 6.4 27 22 18 25

37 31 30 45 38 40 36 36 52

36 40 37 42 51 36 41 37 38 51

38 41 39 39 53 36 39 42 40 42 52

37 38 41 40 42 51 36 40 41 42 42 50

31 36 41 42 41 42 48 32 37 40 43 44 44 48

32 38 42 43 43 47 49 33 38 42 44 44 43 48

35 38 45 43 42 44 48 42 44 52 53 53 54 29

19 39 46 55 53 52 53 27

48 52 57Efficiency

-110 1

310

410

43 43 34 56 48 51 43 64

48 51 44 64 49 46 52 48 64

51 48 52 51 62 47 50 51 47 62

51 51 54 49 62 53 50 49 53 51 60

52 50 51 53 49 63 51 50 52 54 48 60

53 51 51 53 53 48 57 57 51 51 53 55 46 58

54 52 51 55 54 49 56 50 52 51 54 52 46 53

50 52 53 54 49 42 52 62 61 61 64 59 51 52

59 62 62 62 63 53 43 14

59 43 24Purity

Figure 8: The efficiency and purity in % for each bin are shown for 99-00 e+pdata.

36

ZEUS

X

)2 (

pb

/GeV

2/d

xdQ

σ2 d

-110

1

102= 648 GeV2Q 2= 761 GeV2Q 2= 891 GeV2Q 2=1045 GeV2Q

-210

-110

12=1224 GeV2Q 2=1431 GeV2Q 2=1672 GeV2Q 2=1951 GeV2Q

-410

-210


-610

-310


0.5 1

-710

-410

2=9055 GeV2Q

0.5 1

2=14807 GeV2Q-1=300 GeV L=39 pbsp +ZEUS NC e

-1=300 GeV L=39 pbsp (int.)+ZEUS NC e

68% CL limit

SM NLO CTEQ6M

Figure 9: The double-differential cross section for 96-97 e+p NC scatteringat

√s = 300 GeV (solid circles) and the integral of the double differential cross

section (open circles) compared to the Standard Model expectations evaluated usingCTEQ6M PDFs (lines).The error bars show the statistical and systematic uncer-tainties added in quadrature. For bins with zero measured events, a 68% probabilitylimit, calculated including the uncorrelated systematic uncertainty, is given.

37

ZEUS

X

)2 (

pb

/GeV

2/d

xdQ

σ2 d

-110

1


-210

-110

1 2=1224 GeV2Q 2=1431 GeV2Q 2=1672 GeV2Q 2=1951 GeV2Q

-310

-210

-110


-510

-310

-1102=4145 GeV2Q 2=4806 GeV2Q 2=5561 GeV2Q 2=6966 GeV2Q

0.5 1

-710

-510

-310

2=9059 GeV2Q

0.5 1

2=15072 GeV2Q-1=318 GeV L=17 pbsp -ZEUS NC e

-1=318 GeV L=17 pbsp (int.)-ZEUS NC e

68% CL limit

SM NLO CTEQ6M

Figure 10: The double-differential cross section for 98-99 e−p NC scatteringat


section (open circles) compared to the Standard Model expectations evaluated usingCTEQ6M PDFs (lines). The error bars show the statistical and systematic uncer-tainties added in quadrature. For bins with zero measured events, a 68% probabilitylimit, calculated including the uncorrelated systematic uncertainty, is given.

38

ZEUS

X

)2 (

pb

/GeV

2/d

xdQ

σ2 d

-110

1


-210

-110

1 2=1224 GeV2Q 2=1431 GeV2Q 2=1672 GeV2Q 2=1951 GeV2Q

-310

-210


-510

-310


0.5 1

-710

-510

-310

2=9059 GeV2Q

0.5 1

2=15072 GeV2Q-1=318 GeV L=66 pbsp +ZEUS NC e

-1=318 GeV L=66 pbsp (int.)+ZEUS NC e

68% CL limit

SM NLO CTEQ6M

Figure 11: The double-differential cross section for 99-00 e+p NC scatteringat


section (open circles) compared to the Standard Model expectations evaluated usingCTEQ6M PDFs (lines). The error bars show the statistical and systematic uncer-tainties added in quadrature. For bins with zero measured events, a 68% probabilitylimit, calculated including the uncorrelated systematic uncertainty, is given.

39

ZEUS

X

DA

TA

/TH

EO

RY

(CT

EQ

6M)

11


11


11


1

10

1


0.5 1

1

10

0.5 1

1

102=9055 GeV2Q

0.5 10.5 1

2=14807 GeV2Q -1=300 GeV L=39 pbsp +ZEUS NC e-1=300 GeV L=39 pbsp (int.)+ZEUS NC e

68% CL limitCTEQ6MZEUS-SZEUS-JETS

Figure 12: Ratio of the double-differential cross section for 96-97 e+p NCscattering (solid circles) and the integral of the double differential cross section(open circles) to the Standard Model expectation evaluated using the CTEQ6MPDFs. The inner error bars show the statistical uncertainty, while the outer onesshow the statistical and systematic uncertainties added in quadrature. The ratioof the expectations using the ZEUS-S and ZEUS-JET PDFs to those using theCTEQ6M predictions are also shown. For bins with zero measured events, a 68%probability limit, calculated including the uncorrelated systematic uncertainty, isgiven.

40

ZEUS

X

DA

TA

/TH

EO

RY

(CT

EQ

6M)

11


11


11


1

10

1


0.5 1

1

10

0.5 1

1

102=9059 GeV2Q

0.5 10.5 1

2=15072 GeV2Q -1=318 GeV L=17 pbsp -ZEUS NC e-1=318 GeV L=17 pbsp (int.)-ZEUS NC e


Figure 13: Ratio of the double-differential cross section for 98-99 e−p NCscattering (solid circles) and the integral of the double differential cross section(open circles) to the Standard Model expectation evaluated using the CTEQ6MPDFs. The inner error bars show the statistical uncertainty, while the outer onesshow the statistical and systematic uncertainties added in quadrature. The ratioof the expectations using the ZEUS-S and ZEUS-JET PDFs to those using theCTEQ6M predictions are also shown. For bins with zero measured events, a 68%probability limit, calculated including the uncorrelated systematic uncertainty, isgiven.

41

ZEUS

X

DA

TA

/TH

EO

RY

(CT

EQ

6M)

11


11


11


1

10

1


0.5 1

1

10

0.5 1

1

102=9059 GeV2Q

0.5 10.5 1

2=15072 GeV2Q -1=318 GeV L=66 pbsp +ZEUS NC e-1=318 GeV L=66 pbsp (int.)+ZEUS NC e


Figure 14: Ratio of the double-differential cross section for 99-00 e+p NCscattering (solid circles) and the integral of the double differential cross section(open circles) to the Standard Model expectation evaluated using the CTEQ6MPDFs. The inner error bars show the statistical uncertainty, while the outer onesshow the statistical and systematic uncertainties added in quadrature. The ratioof the expectations using the ZEUS-S and ZEUS-JET PDFs to those using theCTEQ6M predictions are also shown. For bins with zero measured events, a 68%probability limit, calculated including the uncorrelated systematic uncertainty, isgiven.

42

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